I apologize.. I read your post as if you were getting a new trolling motor AND new batteries. If what you have is a 12 volt, it can't be changed unless you replace the motor and that wasn't in the scope of what you really were asking about. You could run two batteries in parallel and get close to twice your time on the water with it. In that case you are doubling the available current (amps) instead of doubling the available potential (volts). Many people do this with great success and I've done it with my first bass boat.
You won't gain the efficiency of a 24 volt system. That gain, in simple physics terms, comes from the power formula and current loss to heat. P=V*A If you double the voltage, you only require half the current for the same amount of power. With using half the current for the same amount of power the amount of power lost to heat is cut in half as well. There are other factors like wire size and connection quality, but this is just to give you an idea of how a 24 volt system improves efficiency.

For you, if you want to double what you have now, get two IDENTICAL batteries for the trolling motor instead of one. Get a good quality short red battery cable and a good short black one. Make sure you get the right terminal connectors on your cables. Hook the two positives together with the red cable, along with your motor's positive cable. Hook the black cable to the two negative terminals of the batteries along with the TM's negative cable. As simple as that, you've almost doubled your time on the water.