Parents pay for these trips. When a team travels, it will usually be a combination of booster fundraising and parents paying. School budgets across the US are so tight that it is almost unheard of to have a school fund extra trips for sports teams or band, etc.
When there is scholarship money on the line, parents really cannot afford to NOT send their kids to these events. A free ride is worth about $200k+ these days. A few thousand in plane tickets, hotels, rental cars etc. is nothing in comparison. In fact, compared to other sports, the investment you have to make in runners is pretty cheap. Parents will spend close to six figures on kids who are playing tennis tournaments on the national level. There is a volleyball team in my area that parents pay $18k a year to get their kids on. And even in the sports like baseball there are all these all star invite teams where parents have to pay a lot of money to get their kids in front of scouts for college and the pros.