I would recommend a trike or big wheel - absolutely! They each have their advantages. I was particularly fond of my son's big wheel because it was noisy on hard surfaces. I could be in the house and know exactly where he was!
At three she is not ready for a bike!!!!! Sure, she might be able to pedal the thing and make it go - but she does not have the brain maturity to anticipate danger and react in time. (We have all seen the TV videos of little kids riding 2 and 4 wheelers and cluelessly running into trees, cars or over their siblings. Those videos are the ones where no one gets hurt.)
The mechanics of a trike are very simple. You pedal and you move; you pedal faster and you move faster; you stop pedaling and you stop moving. With a bike you pedal and and you move; you pedal faster and you move faster; you come to a slight down hill and you don't do anything and you move faster; you stop pedaling and you keep going; you push back on the pedal or squeeze the levers on the handles and you stop? (That's logical?)
For me, having a bike is one of those milestones. It's something a child really, really wants for quite a while, but has to "earn" it with behavior and actions - proving they are ready for the responsiblity of a bike. Having a bike means a child is ready for a little bit of independence.