It depends on who you are dancing with. If say you are with a chain you may end up paying more than if you are in an independant.
My info is a little bit old. I haven't competed for years. I'd rather spend my money on honing my ability. But it can be a really good tool for many people. Do at least one and see if it's a positive experience for you.
If you are traveling you will have to contribute to your pro's travel costs. If you are the only one going than expect to pay all his/her costs.
You will have to pay an entry fee for the competition. That will depend on the comp. It tends to be between $600-$800 per comp (Independent comps). Than you pay per dance. My pro doesn't charge per dance but I think that makes him rare but you still have to pay entry fees.
You can also enter (if you buy enough regular dances) the scholarship comps and those are more like the real thing. You are actually competing for a prize and not everyone gets a pat on the back. You dance until eliminated. That isn't as expensive and its more rewarding at least for me. Some pros won't let you if they don't think its goign to be a positive experience (i.e. you're going to get slaughtered).
Again things may have changed I haven't been in a comp for a long time, but I imagine prices only went up, not down. You can go to the comps individual web sites to get more specific info.
Good luck!!
