I get a bus at least once a day and the train a few times a week and have never had an issue, and I have a fairly large bjcs. I suggest avoiding peak times with a pram anyway, but I've never found the spaces available already filled. On a train you should try to find an empty space to park so people don't have to go around you, though I doubt you'd be kicked off! On buses you'd nor be allowed to block the aisle.
Good luck, once you get used to it it's no problem, and it's not as hard as you imagine it will be!
sent from my magical device