You can make an estimate based on how much your hot tub temp drops in a given time, which is directly related to the insulation of your hot tub and cover.
It takes about 2.44 watt-hrs to heat 1 gallon of water 1 degree F. As soon as your heater shuts off for a cycle, turn it completely off and measure the temp drop over 24 hrs. If you calculate that your tub drops 20 degrees in a day, then you can calculate as follows:
2.44 watts x 20 degrees x 350 gallons = 17 kw-hrs. x cost of electricity = $/day.
There is a lot of simplification here, so your usage is going to be more in reality, but this should give a close approximation on what it costs to maintain your temp. The greater your temp drop over the 24 hrs, the more off your calculation will be. Variables are outside air temp, how much you use the hot tub, efficiency of the heater, etc.
A more accurate way to calculate would be to monitor how long your heater runs every day, but that is usually difficult to do manually, so that is where the kill-a-watt or a simple hour meter comes in handy.