you can set the speed limit a bit higher to avoid the motor cutting out, that won't affect the battery consumption. When you come home, note down the time it takes to recharge your battery. You could do the same with your wife's bike. The longer it takes for the charger to go green, the more battery the trip has consumed. If your battery takes longer to recharge than your wife's, then your GSM kit consumes more than the Batribike.
Your battery has 11.6AH capacity, it will take about 5 hours 40 minutes to charge from 0% left to 100% full. Knowing how long it takes to recharge for the trip, you can extrapolate how far you can go before the battery runs totally flat.