Hail of Blades + Shield Bash
The idea is to jump off of your carry when your passive and HoB is available, auto the enemy once to gain the shield / mana. The bonus attack speed makes it relatively safe to get the second auto attack off to deal bonus damage from Shield Bash. The third auto really isn't too important to get off because Yuumi's auto attacks aren't that strong. Instead, just jump back on your carry and give them the shield.
With HoB on a 4 second out of combat cooldown and Yuumi's passive on a 20 - 8 second (based on level) cooldown, and with the 80 - 360 (based on level) +40% AP shields, .. this strategy basically turns Shield Bash into your keystone.
Alternatively, you could go for Lethal Tempo for the bonus attack speed, but the 1.5 second delay in attack speed means you need to use Q before you jump off, or you'll see just how dangerous 1.5 seconds of being targetable as Yuumi can be. It just seems really risky, and potentially awkward to me.
Or, you could try to get the attack speed from items, but that doesn't seem efficient. I would rather invest in AP, which would increase my shield and heal size.