Is it the Vertex/Yaesu VX-700 radio? I don't know much about amateur radio but I know a few pilots who carry this one because it's also an aviation navcom. It's a pretty slick unit, rugged, waterproof and fairly compact.
If I were you, I would probably get the vinyl case for it and modify the case. Cut two slits in the back of the case and thread velcro straps through crosswise. Then cut two more slits perpendicular near the top and thread velcro through as well. Then mount the case on your stem with the top near the handlebar using the crosswise velcro to secure it to the stem. Use the other two velcro straps hanging from the top to secure it to the handlebar. You may also wish to consider taking a thin but fairly rigid piece of plastic cut to the shape of the transciever to use as a backing for the vinyl case to make inserting and removing easier. Good luck.