Place the water pump next to the full bathtub. While it is not practical to hook a pump up to the tub permanently, you can store the pump under the sink in the bathroom and bring it out when you need to drain the tub.
Connect a hose to the intake valve of the pump and place the other end in the deep end of the tub. The hoses can be left on the pump as long as they're dry so you don't have to reconnect them with each usage.
Run a second hose from the outlet valve to the sink. This helps divert some of the water to the sink drain and therefore increases the overall draining speed of the bathtub.
Turn on the pump as the tub drains. Monitor the water in the sink to ensure it doesn't fill faster than it drains because then the sink may overflow. Turn off the pump if this happens to give the sink time to clear and then turn it on again.