I believe that the 38 is supposed to have .358 diameter at the groove depth, the top of the lands will vary with whatever degree of wear there is on the bore. But, all that is subject to whatever mood the machinist who made it is in. As an example, I have a 32-20 that is made with a .309 bore because TC made them to fit .30 caliber bullets. I bought it used and it has a measurement .311 slugged. It's not "what it's supposed to be" that counts, it's what it really is.
And Lone Star is right, if you've never gathered up a mallet, extra cleaning rods or dowels to slug a barrel, you may as well start. The pistol in my picture, I slugged it twice. I stuck a couple of bullets in the barrel, tapped them out. Shot a couple of bullets COMPLETELY through the box of rags, etc. The powder I used was 4759 but, that doesn't matter. With one bullet, it was fine. When I changed to a lighter bullet weight, then I shot it through the rags into the ground! I had to drop the powder charge to accomodate the measuring process. -All of this is subject to how much tinkering and experimenting your patience will stand-
If you're buying bullets, a 38 is .358. If you're casting your own and sizing them, you can still use .358 and go as big as .362 (.360 being good). As soft as lead shoots, it isn't finicky or picky about size unless it's undersized and then, it gets inaccurate at some point. I just size mine to specs and if they don't shoot good then, I'll oversize them the extra 2 thousandths. Just relax, think, and err on the side of caution. A cool head and calm disposition can accomplish a lot. Never be in too much of a hurry to think about the task twice and do it once. Good Luck