What's with this speed thing. More can be done with one well placed long note, than 20 ill placed notes... It's important to be comfortable with what you have..
Improv comes from doing just that. Play whatever to everything you can find. If you go at it nice and slow, you will find yourself throwing in things as time goes by.. It takes a bit of time to know where you can throw in a cool trill (simple enough) or rip out an arpagio from hell.