Caterer

Caterer
 

A caterer is a person or company that prepares food usually for parties and events. Dictionaries say abastecedor, but that seems more like purveyor.
Is abastecedor the right word for caterer?

Yes, "abastecedor", "proveedor", "surtidor", are all good, as long as they go with "de alimentos/comida", because those words could be used to a purveyor of any kind. :)

Also, for the specific service of parties and events, in Mexico we would prefer "servicio de banquetes". :)

In Spain I think the most common phrase would be servicio de cátering.

(The TV series Los misterios de Laura had a character whose company was called Catering Zeta Jones, which I thought an excellent pun).

Excellent pun, indeed. :-)

From An English-Spanish Dictionary (Granada University, Spain), 10.2
caterer

(n.) = catering, servicio de restauración
Ex: People who buy foods from roadside vendors or caterers that do not have health permits 'are playing Russian roulette'.