That brings the first question, what tool post are you using?
Dead sharp tool, no top rake, no chip breakers...
How tight does the fit have to be? If it needs to be a precise fit, then measuring that might turn out more challenging than making it...
You certainly could get such a drill bit, but it's going to be more than your lathe wants. And probably tear up the morse taper in the tailstock..... You want to bore that.
You must (within reason, there are ways.... but within reason....) you must drill a hole large enough to let your boring bar enter.
This will leave the "point" of the drill at the bottom of that hole. You can drill the hole to depth "plus the drill point", and after you bore the hole, it'll be flat on the bottom, except that "dimple" in the middle from the drill point.
OR, you can drill the hole to put the drill point exactly at the bottom of the finished hole. You'd then bore the hole, and it will be shallow, but at that point, once it's widened, 98 percent of boring bar options out there will let you "face" the bottom of the hole, bringing the whole thing to depth with no divots in the bottom.
But that's about all we can can give on the boring bar at this point. We've got to know how you're holding it to the lathe before we can give you any solid advice on "which" tool to buy.
Truth be told... At a quarter inch deep- You could grind a boring tool out of a 3/8 HSS blank and plow through that. With a little restraint, you could do it with quarter inch HSS, so another pertinent question might be "Are you getting a job done", or "Is this the job that is a trigger for filling out an incomplete tool collection? Both answers are valid, and warrant very different advice.