Bleach solutions are routinely used in the hall areas of zoos to disinfect including amphibian areas, so yes you can use it if you are careful. Make sure the area is very well ventilated and you want to make sure you are adding the bleach to the water in a bucket as it reduces some of the fumes. I've worked with people that would pour the bleach on the floor and then hose it and the fumes are just murder. The bleach can leave a white residue where it interacts with the concrete but it does come up okay. If you are really worried about the fumes, you can use a cleaner like comet as that significantly cuts down on the fumes while allowing you to get the bleach disinfection, just be warned that it will leave a white residue as it is hard to really wash down a floor.
Don't forget the bleach can be very irritating on your lungs and eyes.
Ed