You're over-thinking this. If you want to know the gallonage then check the meter before and after the fill and that should be within a few hundred gallons (including whatever you've used throughout the fill). The trouble with the 5 gallon bucket method is that your water pressure and flow likely fluctuate significantly throughout the day based on the demand of you and your neighbors.
Your biggest concern should be filling the pool as quickly as possible.
Your biggest concern should be filling the pool as quickly as possible.