If the hidden character can see, they should be able to move out of the way before being run into, unless severely distracted (DM's discretion). If the hidden character is blind (i.e. darkness), then they wouldn't be able to do so, and running into them would end being hidden.
Exactly.
Some years ago, there was something going around where the question was: if you had a choice of being able to fly or to turn invisible, which would you prefer?
I'm firmly in the "flying" camp. The major problem with invisibility is other creatures unwittingly entering the space of the invisible creature. We're not just talking about hostile opponents bumping into you. A bird could slam into you. That stirge hanging in the air having followed your pheromone trail, its belly visibly swelling: that might just be a bit of a tell-tale.
In the RW, crossing the road while invisible could be considered suicidal.
A hidden, invisible creature may well have to pay attention to multiple factors, depending on the situation, and reacting/responding to those can easily be disadvantageous to remaining hidden.
Getting bumped? That's a biggy.