Back in my bluegrass/swing country days I played upright walking on a lot of our set lists. Even did a solo every now and then. 😀
Actually it's not heard much in blues but often in swing, western swing, rockabilly, a lot of Jazz and some country swing like yours.
Delta blues, piedmont blues, more modern blues and blues rock very rarely have a walking line.
BiaB has some great walking acoustic jazz RT's -- they call it "on the fours."

Most of what folks would call swing blues is actually a shuffle and harder, IMHO, to nail than walking.
Shuffles are throughout blues - mostly from the time it went electric.

Good session guys you picked and your chops and tone sound good. Nice clean and even sound (important in walking).
A really remarkable first effort! My only suggestion would be some pick up notes here and there ... particularly on chord transitions.

Fun!

J&B

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