I have done this many times. Bowling Ball Express used to give discounts, and were actually cheaper than USP or FedEx. Last year it seemed as if they were much higher than what you could ship yourself. In the last few years, I have shipped right to the hotel that I am staying at. They will usually accept it, provided you write the information about when you are arriving, etc on the box. Some will do it for free, others will charge you a small fee. It is worth looking into. Call the hotel and they should be able to tell you. You probably won't be the first person to have asked. Unfortunately, shipping back can be a headache, as you usually have to find a UPS store or FedEx location and take the balls there yourself. Of course you could use BBE to ship out with, if you don't want to wander around looking for a shipping store.
I think the easiest thing to do is find a 4 ball box. Put your four balls inside of two different two ball totes, and you are done. It is a little snug but it works. Even if you are shipping 3 balls, you can get creative and put a 2 ball tote, and a single ball tote in the box, and fill up the remaining space with some filler.
Your local pro shop should have some 4 ball boxes, or I think that a 20x20x10 box is a standard size.
Good luck, and bowl well,
"This space for rent"