The 20' has the 48 x 78" mattress, yes? (That's technically a "Three Quarter" size mattress, but with extra length; a whole 3".) I have some lovely 400 thread count queen sheets going unused that I may cut down for my 19' Bambi's 48 x 75" bed (which will mean I can allow for the three or four inch topper I intend to put on the mattress, as well as the luxury mattress cover I found for $25 at Marshalls).
I also found a very inexpensive but lovely quilt at Ross Dress For Less in just the right brown (not too dark, I hope) that I am going to cut down to fit the bed as well, and I intend to miter the corners, as I intend for it to come off the bed entirely for sleeping. (The spread from the factory is cream, and we intend to use the bed for lounging and reading. Good way to get the thing very dirty very quickly.)
Double or Full size sheets are six inches wider than the 48" mattress and will probably be a little short by three inches. You may want to buy a fitted sheet that fits a very tall mattress (most of the taller ones fit to about 22") and hope it'll stretch to fit, or you may want to go with a queen fitted sheet, which is 60 x 80" long, and either cut and sew them to fit, or you can buy straps that go under the mattress to keep them on the bed -- Bed Bath & Beyond carries the extra long ones that run the length of the mattress as well as the ones that go cross ways.
Or of course you can buy the custom ones.
While I generally like duvet covers on my duvet/comforters, I also like having a sheet available for when it's hot. I also really like my down comforters nekkid; it's like sleeping under very warm whipped cream! Putting a duvet cover on it makes it a lot heavier, so having the sheet works for me.
Sheets do make it harder to make the bed, though! If you go with a flat sheet instead of a duvet cover, you might want to get a Queen fitted sheet and a Twin flat sheet, which should measure roughly 66" wide, giving you only 9" on each side to have to tuck in. (Depending on your sleeping styles, that may feel short on each side while you're sleeping, though, especially if there's two of you in bed. A Twin XL, if you don't mind having it tightish over your feet, might keep the sheet in place for longer, as it'll have more tucked under the bottom.)
If you want directions for making a Queen fitted sheet into a Three Quarter sheet, I have some pictures at an old blog of mine
. (Keeping in mind I did those actually on the bed as I had no worktable available to me at the time. With a worktable, I'd probably do it by measurement instead.) No directions, so if you want those, let me know and I'll write them up for you.
And, urm, yes, I get rather into details with this kind of thing. I used to be a personal shopper/bridal consultant at Bed Bath & Beyond. Urm. And, yes, I've been accused of being really A-R about the decor I live in.