Without knowing WHAT is in the bucket, it's hard to give a time frame... I've been leaving my brews on the yeast for 3-6 weeks with great results. I also have more fermenters to use, so I'm typically not pushing to use one before the brew has been bottled... I actually have one empty, with another that should be empty by the end of this weekend, or early next. So that's two carboy's that will be available before the next brew day... I'll also have the Sanke kegs fully ready before then (just need to get more caps to put airlocks in, and a few more airlocks and I'm set)...
You don't HAVE to use a bucket, or specific size carboy (like the 6+ gallon sized) for fermenting. As long as you plan for it, you can use things just a hair over 5 gallons (the 5 gallon carboy's hit 5 gallons before they taper towards the bung hole neck)... Really depends more on what yeast you'll be using, and how IT starts fermenting...