Not always possible, and anyway, I wouldn't want to subject the poor fish to a bus, I mean, as far as I can tell, bus timetables are nothing but a work of utter fiction, and I'd want to get my fish back home ASAP so that it didn't run out of air in the bag.
I know nothing about keeping fish but feel commonsense suggests an hour in a plastic bag full of water juggling around in a backpack will not be a comfortable experience.
But if it is on the bus, or in a car, then the water 'juggles' about due to the forces of motion anyway. The point was that if the bag was wrapped up and not able to move about, then it wouldn't really be any worse. I don't think I'd put it in a backpack though, because if something happened, you wouldn't know until it was too late, but if it was in a small box or similar where you could watch it, then I don't see why not on a bike!
Wouldn't a fishkeeper know this?
The name Fishkeeper is used loosely for people who own fish. I own fish! some rather large (we've had then for years) Goldfish if you must know, and I'll tell you, a couple of them were rescued from somewhere in a bucket, and I defy anyone to see a worse way of transporting fish than bobbling about in a bucket!