It's not really realistic to directly approach Sheik honestly. The MU requires a lot of patience in the sense that you have to force her into a position in which she doesn't have the space to zone you out completely. You just have to nibble down her stage control with the usual empty short hops and shield approaches. Do keep in mind that unless she hard reads a shield approach, she's not going to do a whole lot with it.
In fact, if she doesn't hard read your shield approach it will net you some sort of an advantage that is supposed to lead into something really worthwhile, be it because you're forcing it to the ledge. Getting minor hits in on Sheik leads to ******** setups and big damage, if she gets anywhere above you you are in a situation in which you should consistently be getting grabs or OoS nairs. If you don't land these consistently in this situation you're being either not on-point enough or you're just being severely outplayed (this is a general advice, you exploited these situations appropriately and this is not something you have to work on).
You have safe means of poking her shield with fair, and if you can force a landing in which her front is turned towards you you can bait/punish non-landing aerials with your own fair and bair. rofl that made no sense whatsoever If she has her back towards you you're probably not going to do anything directly substantial to her, her bair will beat anything you have out (unless you get right below her with an upair, of course).
Also note that she is extremely chaseable offstage, especially from below. She cannot afford to space away from the stage unless she wants to risk getting edgehogged. I think you did this fine as well though.