The LRCA (Louisiana Rodeo Cowboys Assosiation) is one association that allows you to enter without being a member. At some rodeos you have to buy a permit which is like, 10$ if I remember correctly. Or you could just join for $100 bucks :). Check their schedule on FB and website. There is at least one rodeo every weekend for the next 4 or 5 weeks with more being added. Laffayette is this weekend but the books have closed.
Check out the Cajun Rodeo Association also. They have fewer rodeos, but they have two separate rodeos Friday and Saturday at most, so you can stay overnight and make two runs.
But they're run very well and the people are friendly. No added $, but great payout! Barrels is around 80%.
Also check the dates for Southern Pro Tour. There are only 3-5, but no membership or permit and great rodeos. $500 added usually in the barrels. They're just on FB I believe. Some were cosanctioned with LRCA last year, but not sure if that's the case this year as well. :)
If you have trouble finding dates let me know and I'll get them for you!