She's a toxic jerk but she does not owe you rides from offsite outings, and neither does anyone else.
You can call a cab or Uber if it's available in your area. That is not her problem, and neither is the lousy bus schedule where you both live.
Only worry about her in the context of work, and talk to your boss or even HR if you are bothered by her. Being skipped when it's time to hand out cupcakes is petty childish nonsense but don't sink to that level by giving a damn about it.
Her crap only matters when it comes to concrete businesslike complaints. Cupcakes aren't even on the same planet as that.
Here's what (and this is by no means an exhaustive list, but it should give you an idea) you can and should complain about to your supervisor or HR:
- Complaints that you did work incorrectly, when you did not
- Taking credit for work you did
- Acting as a supervisor over you when she has no authority to do so
- Racial and ethnic slurs
- Sexist comments (yes, people of the same sex can make them)
- Loud or disruptive behavior making it difficult for you to do your work
- Claims of you being incompetent, made by her
- Her actively working to block a transfer, promotion, or change of duties for you
- Her gossiping about you that disparages your work performance or makes your time at work so miserably uncomfortable that you cannot do your job (this is along the lines of being told you're ugly or lazy or are involved in an affair or something like that)
- If she ever refuses to work with you
See what I'm getting at here? Socializing outside of work is utterly voluntary. You don't have to do it, and not doing it does not and should not affect you at work unless it creeps into something like what I've listed above.
Same is true of socializing within an office and during business hours. You do not have to play the game. Is it nice when everyone gets along? Yes, of course it is. But people do not have to be buddy-buddy.
Go to your supervisor, and talk to him or her. Lay out what happened and have notes, with dates and specifics. If there are emails, then have copies of them. This person being a jerk and not offering you a cupcake is just their own nastiness but your supervisor does not give a damn. But if you are missing out on work opportunities because of this person, then your boss needs to know about that.