You can buy one without a license, you can get yourself a learners license for about £10 I think, there are restrictions as to where you can go with a learners license - mostly, stay off beaches and town area...
Also, when you get your learner's license you need to buy L plate's (stickers) and put it on a visible place on your bike....oh yeah, learners cannot carry passengers....
for bike - check out Friday-ad - they've got a website too...make sure you're on the gibraltar version though.