You could stay in Lexington, Bardstown, or even Louisville and not be too far away from the action.
There are seven stops on the actual Bourbon Trail. Buffalo Trace isn’t one of them. There are also a few smaller distilleries (Willett and 1792 in particular) near Bardstown. You could easily make three days out of it.
The best one by far is Woodford Reserve (aka Labrot and Graham). If you had one day to spend in Kentucky, that’s where I’d tell you to go. They have really cool events all the time (cooking/bourbon/cocktail classes, etc.), so what I would do is find something going on there and plan the rest of the trip around that. The actual tours have gotten pretty crowded, though it’s still very cool.
The only one on the official trail I’d call skippable is Town Branch. It’s cool that it’s in downtown Lexington, but it’s the most expensive tour of the bunch ($8, I think)and it’s kind of half-assed. Their beer (Kentucky Bourbon Barrel Ale, among others) is a way bigger deal than their bourbon, but you don’t even get to sample it (thanks to Kentucky’s weird alcohol laws). And their bourbon kind of blows, IMO. If you want to do the whole Bourbon Trail and get the T-shirt and all you can do it, but I wouldn’t go out of my way.
Buffalo Trace is awesome and definitely worth a visit. You don’t get to try the Pappy there, though–just BT and Eagle Rare, IIRC. (When I was there they had a pack of Pappy labels sitting on a desk next to the bottling line. I thought about taking one but they could tell I was thinking about it and eyeballed me like crazy.) There are plenty of places in Lexington and Louisville that serve Pappy, though.
A lot of the distilleries have more “corporate polish” than I’d like (for lack of a better word). Makers, for instance, used to have a little gift shack with a crock-pot full of wax that you could dip a bottle in, but they moved to a huge shop that wouldn’t be out of place in a touristy mall. It’s still a gorgeous place, though. In fact, the biggest draw of the distilleries to me is that they’re mostly in beautiful places.
October would be a great time to do this, especially if you made plans to slip in a day at Keeneland. You could easily spend three days doing the distilleries. Keep in mind that they don’t all do tours on Sundays, and even if they do they might not be able to give samples.