I'm going to give you an "averaged" costs.
1) Costs per competition - every "comp" is different depending on the organizers.
2) Many give a discounted per entry fee if you buy a "package"
3) A package can be a combination of "hotel room, admission fee to your dancing session e.g., morning or evening", evening show ticket, meals...so you would have to see if the cost of a Package is better for you than paying for everything separately.
4) You would also pay for your "pro" hotel room, his admission ticket, his meals, his travel time, parking for his car...anything
5) Some studios also charge a studio fee...your going to pay the "studio" a fee for competing with the "pro" as they deem it "time away" that they could be earning $$$ in his absence.
6) Hair - your hair will have to be up-do and off your shoulders, get an
appointment with the competition hair vendor
7) Make-up - also Comp vendor unless you know how to do your own stage make-up
8) any accessories your going to purchase to accent your
9) Ballroom competition dress (rental or purchased).
10) Shoes - do not go onto the comp floor with dirty used shoes.
11) Will your "pro" charge his fee per entry or will it be per dance...
12) Will your "pro" charge a "recall" fee per dance or entry if you dance scholarship and your recalled back to the floor to dance again, in addition to the fee per entry that the organizer will charge.
These are things you need to find out from your "pro" before you decide that it's worth it to you.
Many people will compete in a studio vs studio match up rather than an organized competition because it will not break the bank per se and it gives them an idea as to what to expect on a smaller scaled back cost range.
The questions are best answered by your teacher, just remember you will pay all his costs and his charges to dance with him - unless other students are also dancing, then his cost(s) other than the entry per dance fee - should be split amongst the competing students.