Yes, like UnaClocker said, there are several designs for H bridges, even with electromechanical relays.
But I believe there's a simpler "H bridge" with transistors, have you tried this one UnaClocker: (on my next post)
There's no much science behind it, and it only takes 2 transistors. If you're playing with motors up to 2Amps, I would recommend both the TIP122 NPN and the TIP127 PNP.
Regards,
Ulysses L.