Yeah you get Speeder Bikes starting at level 25, and they upgrade at level 40 and 50 into faster ones. There's different models of them as well afaik, at least I know with DDE you get a boss little STAP.
you get sprint at lvl 14 for all classes (out of combat run speed buff) and then at 24 you can buy your first speeder licence. Speeders = mounts. Few to choose from and there are faster ones at higher levels.