I replaced the vanity light. Then replaced both switches. The fan/light come on, The vanity light blows the breaker. There are three sets of wires, all three are black/white/copper ground. I have one set attached to one switch, the other 2 sets are attached to the fan switch.

Disconnect the vanity light, at the light, to determine if the short is the light or in the switches.

I am assuming you put the wiring back exactly as found when you changed the switches.