I'm surprized no one has said Basil Hayden. Made by Beam but is a whole lot smoother with much richer flavor.
Basil Hayden is Old Grand Dad that has been watered down to 80 proof and has a pricetag commensurate with its very nice packaging. It's good, but the Grand Dad 114 (114 proof) or the Bond (100 proof) might be even more pleasing, for about 1/2 the price - and be well under the $40 limit the OP asked for.
You can always add your own water to taste with higher proof bottlings.
Roger
I agree with recommending Bonded Old Granddad. It is a fantastic buy-7yrs old, single barrel,and 100 proof(per us federal law).
...my budget is under $40.00 a bottle...
If you can find some Pappy Van Winkle 20 year Family Reserve, grab it up. It is a very fine bourbon.
My favorite go to bourbon is Four Roses. It is smooth and very reasonably priced. The small batch and single barrel bottles are even better but a little more expensive. Makers Mark is also very good.
With the high temperatures here in Atlanta the last month or so, I have enjoyed some ice cold mint juleps with Four Roses. Absolutely refreshing, hard to describe until you enjoy one in the heat.
Gary
Evan Williams Single Barrel is my absolute go-to when it comes to bourbon. I've tried many bourbons between $25-50 and I've never found anything that I enjoy more. The reasonable price is just a bonus.