Will I get kicked off bus if I take my budgie in birmingham?

I really need to get her to an avian vet tomorrow, she's having respiratory issues since yesterday she's been wheezing, sneezing, moaning and sounds like her nose is runny or blocked but there's no discharge, I'm too scared of going in a taxi alone cos of safety reasons and it'll be expensive for a pet. Also taxi make me feel nauseous as I get travel sickness in cars. National express west midlands buses only allow assist dogs I've asked them on twitter. Google says it's up to the driver idk which is correct. Any advice? I have no other choice, she'll die if I don't take her.

As above it will almost certainly be the drivers choice, but I think most would be unconcerned about a small caged animal going to the vet.
How obvious is it going to be that it's a budgie? like could the cage be covered or placed in a box, just for the time it takes to get on the bus?

Not very obvious, I've got a small carrier like a box bag with a shoulder strap and I can put a dark piece of fabric over it to keep her quiet as she is pretty loud