That’s a kinda hairy way to go about catching the snake.
Given the (mostly) flat surface and a small snake, I would:
Put bucket, upside down, over snake.
Slide flat cardboard or similar under snake and bucket. (Has to be reasonably strong cardboard.) A simple baking sheet that is big enough would work even better. Lift the bucket only enough to slide your sheet in, say, 1/8”.
Keeping the sheet of “whatever” snug to the bucket, flip the combination. Now you have the snake safely in the bucket.
Don’t overestimate the length of snake needed to get out of the bucket! I’d likely dump the snake out of the bucket and into a trash can.
Call Animal Control or transport snake to a wilderness area.
Don’t take chances. Shoot snake in head with small caliber shotshell round if in any doubt whatsoever.
Another option, if Animal Control can come out fairly quickly, is to simply trap the snake under the bucket and put a heavy object on the bucket. Let Animal Control remove the snake.
(If the bucket is in the sun, you’ll cook the snake fairly quickly.)