I don't think there is enough information (like bus speed, braking force, temperature, etc.) to determine the answer. My instinct, though, is that the bee would be able to stop itself before it hit the FRONT of the bus.
Think about the air in the bus. The bee is floating in the midst of an air mass as it (the mass of air) is carried along inside the bus. The bee is able to effect enough force on the air underneath it to keep itself from falling to the floor.
When the bus stops suddenly, the air will want to slosh toward the front of the bus, carrying the bee with it. And here is where the gut feeling comes in: The air mass will be denser at the front of the bus, so, assuming the bus isn't braking with too many G's, the bee should, by shifting its force vector, be able to get enough support from that denser air to keep it from becoming a grease spot on the inside of the windshield.
