So, I see a few different places here where I think can offer advice. 
Free Company story arcs: I'm going to assume for the moment that you enjoy, or think you would enjoy, plot-oriented RP, and that your character has a reason to be in the Free Company ICly. If the former isn't true, and it isn't true for a fair number of RPers, then that's fine; there's no reason to get engaged. If the latter isn't true, then it may be time to find a new Free Company, because this one isn't working for you IC (and possibly OOC).
So, working from the assumption that both of those are, indeed, true, your character has a built-in motivation to engage with the plot. Your Free Company associates are your friends, your family, your employers, or someone else (and if they're not -- if you don't really know them IC or OOC -- see above about how to handle that), so you have a reason to want to engage. In terms of engagement, why not have your character just ask someone they think looks knowledgeable or interesting about what's going on? "Expository banter" is an easy, low-impact form of RP where someone brings you up to speed on a plot. Indeed, I'd say about a quarter of my plot-oriented RP falls into that category. If your character doesn't know or can't guess who might be a good choice, talk to an officer of the FC OOCly and ask them. Chances are, they'll be able to set up RP to loop you in. If they don't want to, or push back on this... see above about how to handle that. 
Walk-ups: Walking up can be hard to do. I, too, typically need an IC pretext, because why would my character just start talking to someone? That said, IC pretexts are easy to work out OOC. RPers who are walk-up friendly are, by definition, putting themselves out there for RP, and a key part of RP is OOC communication. Don't be afraid to send them a tell to the effect of, "Hey, I'd like to RP with you, but I don't know how we'd get them interacting. Any ideas?" You can make this tell more effective if you volunteer some characteristics about your character -- what they like, what would draw them over, what might start a conversation. To use a personal example, L'yhta has an intense interest in various forms of magic. So, if I want to do a walk-up with someone, I'd volunteer that and ask them if they had anything that stood out in that way.
About shyness: L'yhta is a very outgoing individual when she feels in control of a situation, when it's with people she knows, or when it's within her areas of expertise. She's somewhat reserved otherwise. To Nebbs's point, a Manic Pixie Dream Friend can help a lot with working around that shyness. Using another personal example, L'yhta generally avoids large crowds of people she doesn't know in purely social situations (she'll get right up in a crowd of adventurers, but a party at a tavern? A pajama party? A concert? Oh, my, no, never). How I get around this is have some other character that she knows drag her there, either as a friend or as arm candy. That way, she feels more comfortable because she has someone she knows and can interact with -- and hey, if that person ditches her, there's some conflict RP that arises out of that.
I hope this helps! Just from reading your post, I still have to wonder if you've found the right Free Company for you. If they're great, nice people OOC, then I'm sure they'd be amenable to engaging with you OOC to help loop you into the RP more so that your character has stronger connections and better reasons to engage. If they don't want to do that, or if the IC concept of the group (or the characters in the group!) don't mesh with yours, though, it might be time to move on.
As a postscript, I often have times I'm available for random RP, and I can almost always come up with a pretext for two characters to interact. Depending on the situation, L'yhta can even be your Manic Pixie Dream Friend. Feel free to reach out if you want to set something up.
Free Company story arcs: I'm going to assume for the moment that you enjoy, or think you would enjoy, plot-oriented RP, and that your character has a reason to be in the Free Company ICly. If the former isn't true, and it isn't true for a fair number of RPers, then that's fine; there's no reason to get engaged. If the latter isn't true, then it may be time to find a new Free Company, because this one isn't working for you IC (and possibly OOC).
So, working from the assumption that both of those are, indeed, true, your character has a built-in motivation to engage with the plot. Your Free Company associates are your friends, your family, your employers, or someone else (and if they're not -- if you don't really know them IC or OOC -- see above about how to handle that), so you have a reason to want to engage. In terms of engagement, why not have your character just ask someone they think looks knowledgeable or interesting about what's going on? "Expository banter" is an easy, low-impact form of RP where someone brings you up to speed on a plot. Indeed, I'd say about a quarter of my plot-oriented RP falls into that category.
If your character doesn't know or can't guess who might be a good choice, talk to an officer of the FC OOCly and ask them. Chances are, they'll be able to set up RP to loop you in. If they don't want to, or push back on this... see above about how to handle that. Walk-ups: Walking up can be hard to do. I, too, typically need an IC pretext, because why would my character just start talking to someone? That said, IC pretexts are easy to work out OOC.
RPers who are walk-up friendly are, by definition, putting themselves out there for RP, and a key part of RP is OOC communication. Don't be afraid to send them a tell to the effect of, "Hey, I'd like to RP with you, but I don't know how we'd get them interacting. Any ideas?" You can make this tell more effective if you volunteer some characteristics about your character -- what they like, what would draw them over, what might start a conversation. To use a personal example, L'yhta has an intense interest in various forms of magic. So, if I want to do a walk-up with someone, I'd volunteer that and ask them if they had anything that stood out in that way.About shyness: L'yhta is a very outgoing individual when she feels in control of a situation, when it's with people she knows, or when it's within her areas of expertise. She's somewhat reserved otherwise. To Nebbs's point, a Manic Pixie Dream Friend can help a lot with working around that shyness. Using another personal example, L'yhta generally avoids large crowds of people she doesn't know in purely social situations (she'll get right up in a crowd of adventurers, but a party at a tavern? A pajama party? A concert? Oh, my, no, never). How I get around this is have some other character that she knows drag her there, either as a friend or as arm candy. That way, she feels more comfortable because she has someone she knows and can interact with -- and hey, if that person ditches her, there's some conflict RP that arises out of that.
I hope this helps! Just from reading your post, I still have to wonder if you've found the right Free Company for you. If they're great, nice people OOC, then I'm sure they'd be amenable to engaging with you OOC to help loop you into the RP more so that your character has stronger connections and better reasons to engage. If they don't want to do that, or if the IC concept of the group (or the characters in the group!) don't mesh with yours, though, it might be time to move on.
As a postscript, I often have times I'm available for random RP, and I can almost always come up with a pretext for two characters to interact. Depending on the situation, L'yhta can even be your Manic Pixie Dream Friend.
Feel free to reach out if you want to set something up.
The Freelance Wizard
Quality RP at low, low prices!
((about me | about L'yhta Mahre | L'yhta's desk | about Mysterium, the Ivory Tower: a heavy RP society of mages))
Quality RP at low, low prices!
((about me | about L'yhta Mahre | L'yhta's desk | about Mysterium, the Ivory Tower: a heavy RP society of mages))
