Ti is used in bicycle frames all the time. It takes special tools and a special welder, no big deal for people like
Seven or
Moots or even
Litespeed. The welds on those bikes (well, Seven and Moots) are a work of art.
Ti is not as stiff as steel for a tube of the same thickness and diameter, but it weighs roughly half of steel per cubic centimeter (less dense in engineer-speak). A designer can increase tubing thickness and diameter and get a bike that is both more stiff with less weight. See
here.
Ti is not brittle. Depends on the alloy. It flexes and has great memory. Eyeglass frames are made of Ti because they can bend without breaking when someone sits on them. If someone can whack a Ti bolt and have it snap off, either you are superman or it's a really cheap bolt (or really tiny).
So why not a Ti motorcycle frame? I dunno, but a good Ti bicycle frame is in the $3000+ range so that might be a clue. Motowheels wants $1300 just for a simple Ti subframe.