Women have been riding rough stock in open rodeos for as long as there have been rodeos. When things got organized with the old RCA (rodeo cowboys assoc.) and IRA (international rodeo assoc.) clubs, women organized and started the GRA(girls rodeo assoc). When RCA became PRCA, the gals went to WPRA. I rode bareback in open rodeos and bareback in the slack in RCA rodeos.
As long as a lady is willing to ride one-handed (much better, IMO) and go the 8 seconds, I'm all for them competing with the guys.