At instrumental sessions, I'm rather shy about my abilities (or lack thereof) as an instrumentalist, so I'm happy to hide in a corner and try to play along softly.

That's exactly backwards. If you're less technically able than most of the people around you, it's much better if you do lead as much as possible, because that way you'll be playing at your best and they can reinforce you, at a pace you're comfortable with. Try to follow all the time and it'll feel to them like you're getting under their feet.