Look on the web at the XC schedules for your school and schools nearby that are within driving distance. Except for a conference or regional meet, most coaches will let you run unattached. You should e-mail the coach ahead of time, and you might have to pay $10-20. If you think you are good enough to run a college meet unattached, you might be able to talk to the coach about working out with the team and running some meets unattached as a way to get the team experience w/o a big commitment.
This is relatively new, but some colleges are offering XC as a club sport. When a varsity team has to limit roster size (or a men's team has to be cut for Title IX), then a school may have a club team that is cheaper to fund.
Depending on where you live, your USATF association may sponsor club-level races that you can get into.
Also depending on where you live, there may be a local running club that will host an XC race (or series).