Three years is nothing for a strelitzia. Ours took at least five years to flower, but after that it has produced flowers every year, and with increasing numbers each year, so it's well worth waiting for.
What size pot have you got it in? Many people underpot these plants and they require loads of space, so pot gradually into at least a 14 inch pot as it grows. They flower when the thick fleshy roots are absolutely crammed into the pot, but they must be a good size to start flowering.

Also, they are unlikely to bloom without at least a few hours of direct sun a day.