Bounce Back's effect states:

R: After your opponent plays a response, your attack gets +X speed. X equals the difficulty of the response's card.

If you use this during the block step after the block difficulty has been decided upon, say if your opponent blocks with an attack and uses the response on Soul of Ling Sheng Su to give the check +2, will altering the speed of the attack have any affect on the difficulty of the block at this late stage?

Once the block step has started at the block difficulty determined, then a control check is made against that difficulty. If you increase the speed after the difficulty has been determined (such as in your example) it will not affect the difficulty of the control check. If your opponent plays a reaction during the block step, but before the difficulty has been decided, such as with Strife's Patronage or Superior Witch, then you can react for additional speed, which will affect the difficulty of the block.

How about Bounce back against responses before your attack is played, so if my opponent plays say forethought/blood runs true/ akuma response, or if they play responses during their attack, would bounce back create a floating speed bonus that would be applied when I play an attack?

Thought as much, but a man can hope.

A man can hope...

Side question:

If you have a multiple copy out, and your opponent uses a response during the original attack, can you choose to have the multiple copy receive the speed pump? Bounce Back says "Your attack", it doesn't say "this attack" and a multiple copy is a recognised entity in the card pool that is awaiting resolution.

EDIT: Sorta ninja'd by Kiit.

The copies can't get speed boosts, bonuses/penalties will only apply to the attack currently resolving.

Vs. CC Hax, the attack isn't in the card pool yet so there's no target for CC Hax.

Other than that, stamp for the block step stuff. Once blocking difficulty has been determined and the check made, the difficulty is set and will not increase.

why wouldn't bounce back create a lingering effect that kicks in the next time you play "your attack" ?

Tagrineth said:

How about before the check is made? Say if they used the R on Strife's Patronage to return the speed to printed before making the check, if you triggered Bounce Back at this point would the difficulty of the block increase?

I covered that in my original post, which got stamped. Since Strife's reacts before the block difficulty is determined, to alter the speed, you can then react with bounce backs to pump the speed, after which the block difficulty will be determined.

kiit said:

Why would it?

By that logic, any "your attack" enhance could arbitrarily be "held" until some future attack of your choosing.

so... no.

The only reason Evil Plans works differently is Voodoo Magick (and the wording "that attack").