Ricochet buffs your next auto-attack, so it will trigger her passive but only on the first hit. Subsequent bounces will not continue to trigger the passive. If I'm not mistaken, her first hit will proc item effects and otherwise act as a normal auto-attack.
Sivir's Boomerang Blade can be an annoying harass, both at early level and late game. Unfortunately, it mostly takes practice to be able to avoid it. But there are a couple of tips that I think (hope) will be helpful in the long run.
Placement
Sivir's Boomerang Blade has a fairly large attack radius. Where you are in relation to where Sivir is when she launches the attack can make a fairly significant difference. The important thing to remember, though, is the further you are from her, the longer you have to react. Try to remain at a distance as much as possible when facing Sivir; especially in early game. One more important point on placement, the more minions between you and Sivir, the less damage you will receive if Boomerang Blade hits you. Each enemy it hits makes the damage to the next enemy lessen.
Movement
Unfortunately for you, sometimes dodging her initial attack ins't always enough. Her blade will track with her, if she moves up or down on the battlefield. You should always move in the opposite direction from Sivir. In the following image, consider your Champion to be X, while the colored arrows show the path of the blade upon return, in relation to Sivir's movement.
One last point worth mentioning is this: While the camera is zoomed in in that image, it's important to remember the high range of Boomerang Blade. It will extend to the far edge of the screenshot.
If you can't always avoid the first shot, pay close attention to avoiding the return strike. But in the end, it really comes down to practice, practice, practice.
Best Answer
For spellshields a Syndra ultimate is basically just a bunch of spells fired in rapid succession. This means that a single orb will be blocked while the other ones just pass through.
As an example: You are Sivir and you use the shield before Syndra uses her ult on you. 4 of the 5 orbs will pass while the first orb gets blocked.
If you use your shield after Syndra has already started casting her ultimate, 2 of the orbs will damage you, one is blocked and the other 2 will damage you again. So basically there is always only One blocked orb.
The same rules apply for banshees and Nocture spellshield.
To prevent burst it's still better to use the shield on one of her other abilities (or best: her stun) since these deal more damage than a single blocked ultimate orb.