bucket as mash tun?

I've heard of this being done before, but I'm curious to know if there are any modifications that need to be done. I'm assuming a large grain bag will work in lieu of a false bottom, but how do I go about insulating the bucket while mashing? Also, how does sparging work with this method? Any help would be appreciated. I'd love to start doing all-grain, but space is at a bit of a premium at my apartment. This would be a good way to get into all grain without the investment in buying and modifying a cooler that I don't have the space or money for.

Yup, it's been done before. Google Papazian zapap. (yes, seriously...zapap)

http://brewingtechniques.com/library/backissues/issue6.5/depiro.html

It's an old methodology, but it would work.

Is there a way to do it without drilling holes in one of my buckets? I'm thinking about wrapping it in packing insulation or reflective foil. Would that work?

Well you need to strain the grain from the wort somehow. That's what the holes are for in the zapap system. You could also do a variant of BIAB where you stick a bag in a bucket and mash there. Or, if you've got a spigot, I suppose you could also do a stainless braid, manifold, or false bottom in the bucket, too.

You would definitely need some kind of insulation, I'd think. Even a sleeping bag or similar ought to work fairly well, I'd think. Also, you'd want to preheat your bucket or put your strike water in there a bit hot to warm it up to mash temps first.

I use an old 5G bottling bucket w/ spigot as a mash tun for now and have been for quite a while.

Mine has the old Phil's Phalse bottom (not even sure they are available anymore) and I wrap it in a quilt. It holds temp for even 90 minute mashes within a degree or so. As for sparging, sometimes I use a sparge arm, other times just fill and stir. Both work equally well and keep me in the 73%-75% range. It's simple, ghetto and it works.

You definitely could use that bucket with "brew in a bag" system or if your boiling pot is big enough you can mash right in there. I merely wrap a thick bath towel around my aluminum pot after mashing in and never have to move it from the heat source, just turn it off. It only loses 2 or 3 degrees over the course of an hour and since most of the conversion should be done in 20 minutes, I don't care if it does lose a little.

Here is a great thread on doing the "brew in a bag" or BIAB as it gets abbreviated. https://www.homebrewtalk.com/f36/biab-brewing-pics-233289/