My last dentist bonded my four front teeth. One of them broke. Can another dentist rebond it?

Your bonding could be replaced by another dentist.  The color match may be tricky as bonding does have a tendency to discolor over time.  Have you ever considered having porcelain veneers placed on these four teeth?  The result would be amazing and you would not have to worry about it anymore.  The time to do them would be now since one of them is broken.  Good luck.  

Yes, another dentist can rebond your tooth.  It is not always easy to get a perfect color match to older bonding.  Bonding tends to discolor over time which is why ceramic veneers are usually considered more permanent.

Yes, most dentists do some kind of direct composite bonding.  However, to get the best result it would a huge advantage for your new dentist to use the same bonding material in the same shade (color).  There are virtually hundreds of different kinds of bonding materials and scores of different shades, all that might give a different result.  My suggestion, if you are able to see the dentist who placed or original bonding, return to him/her.  If not, ask your new dentist to call him/her and find out the name and color of the bonding material used.  Or, better yet, you call the dentist and get that information, and call around to find a dentist who uses that same material and has the same shade.