Basically it is not wise to let your beagle off leash. Our first beagle roamed the area, but we were ignorant in those days. Our last beagle, Spotty, was hell off the lead, so after waiting a few hours for her to return to us we said no more. Our present two cant be allowed off leash, they would panic and be off. I think your beagle might be frightened of losing you, if you are mountain biking. So you are probably safe doing this with him off leash. However, I wouldnt like to guarantee he'll still be near you, if a rabbit runs past or he smells a deer!!!