Removing the bleed effect make this zombie no different than Fast Zombie so it means remove this variant altogether.
My Nerf Suggestion v2
We could lessen its HP just i suggested, bleed stack should not exceed 10 seconds max, and initial movement speed is -50% and they have to continuously move for small seconds in order to regain normal Fast Zombie speed and it resets when you stopped moving; or
They move much more slower when holding left click than a regular Fastie holding left click like -40% slower So when they hit you once, you can run off their range with ease without needing to use your Boomstick, unless your HP is below 30 HP Threshold