Why does my furnace drip bucket fill up so frequently?
Depends what it's dripping.

If it's a high-effiency condensing boiler (despite not usually boiling the water these days, a central heating device that heats water is referred to as a boiler, while furnace refers to those that heat air, in the usual vocabulary), it may be dripping condensate (mostly water) from the exhaust. This often has a somewhat purplish coloration (just as a possible diagnostic/disambiguation point) from the non-mostly-water fraction. Those are usually directed to a drain, or to a collection bucket with a condensate pump that pumps to a drain.

It could also be a straightforward leak, (usually) from an overpressure/overtemperature valve - look for that type of valve on the pipe that is dripping. If so either the valve is faulty and needs to be replaced, or the furnace controls are slightly out of whack causing it to actuate.