If your motor is small enough to be driven directly, you can use two outputs from your ATTiny to reverse the motor. If you connect the motor between two output pins you can drive the motor in one direction by putting one pin high while the other is low. Reversing which is high and which is low will reverse the motor. Both pins in the same state will make the motor stop.
It is unusual to build an H-bridge with BJT's, MOSFETs are the preferred active device in these circuits. At the very least, you will need to put some resistors in series with the base of each grounded emitter transistor to limit the base current. On the grounded emitter transistors you will only need 1V to drive that transistor into saturation. On the Vcc Collector transistors, you will need to exceed Vcc by at least .5V (probably more) to keep them in saturation or reduce the collector voltage by that much. The Vcc collector transistors will self regulate to some degree, since the Emitter-Base voltage will drop as the transistor approaches saturation, the emitter voltage in reference to ground will never exceed about Vcc-1V which should allow the motor to run but not at full speed. If you run the ATTiny on 5V and use a 3V motor, this could work okay. ATTiny claims to handle 40mA per output (200mA max total device current) so if your motor is less than that, you're all good.