Any turf would need to be left in place for a few weeks (maybe a couple of months?) to allow it to root before it is OK for normal use. By this time, it should have had at least a couple of light trims, so should, in theory, be safe for bunnies- as long as the cut grass has been removed and not left to compost in. New turf is often grown on a very sandy substrate which won't hold on the herbicides / pesticides for long - they will wash through. It's only the residual stuff in the actual grass that you would have to worry about - hence disposing of the first few cuts. New turf that hasn't had time to root in position will get trashed by bunnies anyway.
You could try seeding the bald patches - I would sow a lot thicker than normal to get a quicker cover. Bunnies would have to be kept of those patches until it was firmly rooted eg by fencing it off or putting a raised mesh frame over it. You could also grow your own turf in seed trays - then you know that it has no added herbicide / pesticide. Keep it well watered in a slightly shady spot so it doesn't dry out.
Some grass seeds may come with a toxic coating, though - so check the packaging first.