I get nervous going to new things and so have found I really limit myself (and therefore bubs as well) to just the one group I know and feel comfortable with.
One of the things I did enjoy though with minimal stress was going to Rhyme Time at my local library. It was just a free half hour sing-along type thing and to be honest I didn't really get the courage to chat to people much, but LO really enjoyed it and because of how it was set up it didn't matter I wasn't chatty. I know that wouldn't help you make some 'mummy friends' but might be a good stepping stone to build up confidence to go to other things. In the holidays people always took older siblings too, they loved it
