What does bonding on teeth feel like?

It can be natural. A well-done result will feel different since the shape of the teeth may have changed. However, the result can feel very natural, not too sharp and not too rough. It can feel very comfortable. A well-done case will also allow the gums to remain healthy without being reddened nor inflamed and bleeding.
Regular fillings. Bonding usually refers to the chairside composite veneering of the teeth with similar or the very same material they use for simple filings. It initially may feel a bit unusual because it is new, but it won't take much to get used to.
Thicker perhaps. If..When you say bonding on. Teeth i presume you are talking about veneers. Since they are place on top of your teeth they will make them feel thicker but most everyone gets used to them. They may not feel as smooth or slick as your teeth but that mostly goes away too. If you are talking about just a filling being bonded on then it might feel the same but usually not the thick feeling.