how can I build an arduino boat without an h-bridge or bluetooth module?
mabye IR control?
I assume that the boat building will remain up to you and you are actually asking about the boat control.
It is easy to control most DC motors with transistors. If you only want forward motion. For forward and backwards, then the typical solution is an H-bridge.
How will you steer? A servo to control a rudder? 2 motors with differential thrust?
How will you control the boat remotely? Read up on Robin2's Simple nRF24L01+ 2.4GHz transceiver demo
i would use a servo for a rudder.
You cheet your own goals: "without an h-bridge" <-- a servo has an h-bridge.