You don't mention the size, but here are the general guidelines in Texas. Stock 1 to 3 inch bgill from the beginning of September thru December, stock advanced bgill from the beginning of March thru the end of June. The advanced bgill should spawn all the way thru mid October.
Temps really limit the healthy transport of adult fish now, but if you're very close...moving adults now leaves time for a late summer / early fall spawn if all goes well. (Moving adults is my preferred method, I "see" and "select" the broodstock...inferior fish always go up on the bank)