Well I've never cooked a bottom round roast before, but I've done other cuts; prime rib, chuck rolls, etc. and any beef taken to 160 will be past medium IMHO. If you take it to 160 and let it rest it will probably rise to 165-170. If I was looking for medium I'd pull it at 135-140 and let it rest and come up to 140-145 or so, that should be perfect medium.
As always, your mileage results may vary.
As always, your mileage results may vary.