You may need to learn a bit on home electrical. It's not impossible to learn, but it's also not a matter of twisting random wires together until stuff works. (that will more likely burn your house down or get someone electrocuted.) Particularly, school up on all the different ways to wire a "switch loop". There is one right way. There are several ways that will make the fixture light, but are dangerous.
A little learning won't tell you everything, but it will tell you enough to help you narrow it down a lot.
Are the bulbs overloading the circuit or the fixture itself?
Remove ALL the bulbs and connect the fixture properly. The fixture has a hot, neutral and ground. Connect fixture ground to ground always, there's no question or thinking about that. Connect fixture neutral to supply neutral (almost always white). Connect fixture hot to supply hot. Learning to tell the difference between these wires is why I say "school up".
Make sure your supply hot and supply neutral are not connected to each other. That would be a dead short.
A dead short will trip the breaker instantly. An overload will take a few seconds to trip.
If the fixture trips the circuit with no bulbs in it -- it's a bad fixture.
Overload trip or ground-fault trip?
Many bathroom circuits have ground-fault protection. This is designed to save lives if electrical current tries to go through a person, likely killing them. This will also trip instantly. Some breakers will show you whether it's a ground fault trip or an overload trip.
As long as you haven't mixed up ground and neutral, a ground-fault trip on a fixture means it's a bad fixture which can kill people. Back to the store it goes, and don't buy that brand again.
Get rid of the incandescents
They're just too inefficient. They make a lot of heat, which makes the bathroom too warm. This takes more A/C to remove that heat. It drives up your electric bill so much that LEDs will pay for themselves in a year.
I know some are reluctant to convert to new technologies. CFL was a gap technology until they made LEDs work. LEDs are the thing - they aren't going to get replaced by some other technology soon. Color and price are now quite good. Quality LEDs will last 20 years. (of course cheap Home Depot or Costco junk is still junk, you really gotta watch your brands when buying).