I'm in my third year at uni and the only friends I've made are a group of girls (I'm a guy) who were my flat mates in first year, apart from them there's no one for me to socialise with and I've found the last 2 years of uni reall lonely (currently live in a studio whilst they've been in a house). Whilst I'd say they're my best (/only) friends at uni I'm not really in their "inner circle", I'm sure they consider me a good friend but to them I'm not the kind of friend they're really that close to. So far this year they've invited me out twice, once clubbing and once to a restaurant which were the only times I've left my room socially this year. Basically i know in an ideal world I would have made more friends but I've gone past that now with barely 6 months of uni left, my predicament is that I want to hang round with them more but I'm quite shy and have been feeling down lately and don't want to become an annoyance or for them to feel like they have to hang out with me just because I asked.
I want to ask them if they want to do things but because I'm in my own and they are a group of 5, I never have anything interesting to see if they want to do so it's always really me relying on them asking me like hey we're all doing this tonight do you want to come along, I find it's harder as one person asking out a group of 5. Last time I was with them one of them said I was welcome to come round their house anytime and I'm not sure whether to just take that as a passing remark as if I had the choice I'd be there everyday! So in terms of advice as being honest I lack social skills, should I ask if they want to do something or am I right to be worried about becoming an annoyance,I don't want to be a pest and seem like I'm inviting myself round their house even though that's kind of what I want (if that makes sense)?
... and the ones that won't