Firstly, I'm really sorry you had a horrible day...
If it makes you feel better, go into the school office, explain what happened to the school staff about the car parking and the bus and apologise profusely. Then move on from that
Finally, please please very very quickly get out of the mindset that people are dressing up for the school run, or are somehow looking down on you.
Many many people who do the school run, probably the highest proportion, are going straight to work, so aren't dressed for the school run, they are dressed for work.
Some people just dress like that...I blow dry my hair every morning and put my make up on. because I want to do it and its how I work. I'm a SAHM, I don't touch it up all day, but if I didn;t do it forst thing in the morning I'd feel wrong and uncomfortable.
And when I lost a lot of weigh (much now back on) I wore the most gorgeous clothes all day every day...because finally I could...!!! I didn't at any point think negatively about anyone else, or dress like that to make anyone else feel bad. I dressed like that because it made me feel fabulous...!
There is a tiny, tiny tiny % of actual playground bullies amongst the mums...frankly everyone else is just like you, dropping their child off and then getting on with their lives.