From the description it's a 120V device using PWM to run a variable speed DC motor. Since it's AC, you'll need an inverter to convert DC power to AC if you want to run it off battery.
If that's what you want to do, we can somewhat estimate this, but you also need to know how long you'll run it for. For example, let's assume the motor is running about 70% of
@fafrd estimate (it's a variable speed, has a mechanical linkage, an honey is viscous), so...
250 Watts / .7 eff = 360 Watts
The electronics in the "brain" will consume energy too, but we don't know how much... so let's guess 40 watts for 400 watts of AC power.
Now let's say the inverter is 90% efficient:
400 Watts AC / .90 AC/DC = 445 watts DC.
Let's say you run it for 90 minutes a day
445 watts x 1.5 hrs / day = 670 watt-hours/day.
Let say you want to run if off a 12V battery, how many amp-hours would you need?
670 Wh / 12 V = 56 Ah
Let's say it's a lead acid battery and to increase the battery life you want to keep the depth of discharge above 50%, so 56 Ah / .5 = 112 Ah. Then there's Peukert's Law to overcome, since you're draining a battery in 90 minutes rather than 20 hours it would be pretty high, to know for sure you'd have to see the batteries datasheet, usually it's around 50% for such a rapid draw so 112 Ah / .5 = 224 Ah. If you're using lithium instead of lead acid move the depth of discharge to 80% and the Peukert effect to 95% (about 74 Ah).
Considering these are guesses the calculations could be way off. But, hope that walking through the math helps you out.