There are bike computers that transmit the information to a watch. There are also cool ones that
store and graph your speed, etc. (The Brain, I think, specialized?) A google search on appropriate
keywords will get you started.
I've used the Timex GPS watch and it's a decent unit, but here's my take:
It's about as big as a Garmin Etrex. It weighs about the same. The only thing it does that an Etrex
doesn't is give you a pace readout in
min/mile (although maybe you can get an etrex to do this, and for biking, you want mph or
kmph anyway)
It doesn't: map, locate, or do any of the other useful stuff a real GPS unit does, so I think you're
much better off getting a comparably-sized GPS unit. Also, the armband is the only way to secure it
to yourself/bike short of rigging something else, whereas I have seen some nicely-mounted GPS units
on handlebars.