Tap a ball up on the bat a few times, if there's deep seam marks keep going, if not whack a sheet on and get in the nets - sounds like you should have done enough unless the bat is particularly soft!
In ur experience (that is def more than me) are SS bats considered "soft" ?
Don't really have much SS experience I'm afraid! It will vary from bat to bat though, the best way to check is if a leather ball leaves a deep seam mark or not when tapping up - if it does just spend a bit more time knocking in until it doesn't!