Well, there are carrots, which are particularly good for the tops. Ditto with beets and radishes for their tops too. Romaine is also good. Even if it’s overgrown and beyond human consumption, you can pick out the leaves and even the stem for the bunnies.
We’ve found all of these fairly easy to grow. Keep in mind that we have a pretty short growing season at 55.5 degrees north, so I don’t know how this will work in central TX. The house we’re in has a fairly large garden plot, which we’ve planted every year. But for various reasons, we’ve never really exploited it as well as we could so a fair amount of what we intended to plant for ourselves wind up for the bunnies. (“Oops! I guess we really should have harvested the romaine before the stalks developed….well, it’s still good for the bunnies!” “Well, I guess we should have been harvesting carrots every so often instead of most of it all at once…guess the bunnies are getting a lot of carrot tops for the next little while!”)
As far as bugs go, we have a slug problem in our garden, don’t use pesticides (even though Scooter as an environmental research scientist has stockpiles of illegal pesticides in his lab marked “FOR RESEARCH USE ONLY”
, and haven’t done anything special to keep them out. This has hurt some of the leafy vegetables but we can still find enough that the bunnies love. So maybe a bug problem won’t be too much of a drain for bunny greens.
So even if you don’t try all that hard, you can probably wind up growing quite a bit for bunny consumption, if not for you or me.