"Friend's always said she doesn't have a best friend which I respect and understand and I've never asked to be her best friend."
"She has suggested us meeting up alone several times so I know she doesn't hate my company."
"I am literally not going on the group camping trip because I can't bear spending time with her"
"I don't know how to assess my personality/ traits, if its possible to change and if I should/need to."
Wow. Where to start.
Your friend might have had a really tough time choosing bridesmaids. Maybe she has been a bridesmaid for others and felt she had to repay the favour? Maybe she had to choose nieces / step-kids / cousins? Maybe she chose based on their dress size or skin tone (semi light-hearted but I do know women who would do and have done this!)... Regardless, it is her wedding and her choice.
The problems here are with you, not your friend. It sounds like you are extremely insecure with little to no confidence. You can't base your happiness or personality on decisions your friend has made. People always say you can't be happy in a relationship until you're happy within yourself and the same applies to friendships. It isn't fair to put her in a place of being the one responsible for your self esteem and confidence issues.
A lot of what you have written sounds like you are a teenager, not a 30-something woman. Did something happen in childhood that you haven't managed to get over? I would suggest you need to start to see a psychologist to start to unpick some of the reasons why you feel the way you do.
FWIW my best friend didn't pick me to be her bridesmaid! She had her DD, DSD, best friend from childhood (who she was bridesmaid for) and her cousin. I wasn't offended and it has never affected our friendship (10 years on). I don't think we've even mentioned it?! Weddings are stressful and hard to plan. Don't make things more difficult for your friend.