Alas, Disney's view of cycling is to go very slowly along a one mile path. The bikes they rent aren't good for much more than that. And while it is perfectly legal to bike on most of the roads within Disney property, Disney basically hides that fact and does everything it can to discourage serious cycling. They want you piddling along their designated bike paths.
If your DH is serious, best bet would be to find a bike shop in Orlando and pick something up. This requires car access of Disney property, as well as a willingness to ride on some main roads - pretty much everything immediately surrounding Disney has traffic.