I have kept an eye on my energy bill since getting the tub, and the bottom line is that it costs "a little more" but I dont know quite how much. Not enough more than I'm worried about it after spending a few minutes studying it.  At first I was worried that there was something wrong b/c my bills were up $60-70 compared to last year, but so are energy costs. This is SO not scientific, but here it is:
Month    Increase in KWH/day(compared to '05)
December           2kwh (no tub yet)
January               5kwh (no tub yet)
February             9 kwh (no tub yet!)
March                  5kwh (with tub)
April                    9 kwh (with tub)
May                     7 kwh (wiht tub) 
So........february was particularly cold this year- that might explain the increase with no tub, since the house is heated with electricity. Otherwise, I'm thinking that I have 5-9 kwh/day, or 150-270kwh/month more energy use with the tub. That would be $21-$38/month at my electricity costs right now. FWIW........ 
