Does Amateur Recital save from Ziggs bomb?

No — the move happens, but it doesn't save the unit: the bomb's damage lands first, and lethal damage kills it in the next cleanup even if it's sitting at your Base.

In your Beginning Phase both abilities trigger at once, so as turn player you put Amateur Recital's "when you hold here" on the chain first and your opponent puts the Bomb's Deploy ("when an opponent holds here, kill this") on top of it. Deploy resolves first, the Bomb dies, and its Deathknell ("deal 2 to an enemy there, kill your other Bombs there") goes on the chain above Recital and hits your unit while it's still there. The 2 damage doesn't trash it immediately — a cleanup can't run while chain items are resolving, so Recital then legally resolves and moves the damaged unit to Base, but lethal damage stays marked and the next cleanup kills it wherever it is (Rule 323.4.3b).

Two practical notes: if your unit has 3+ Might the 2 damage isn't lethal, so it survives and the move is pure upside; and if that was your only unit there, you keep the point but lose control of Amateur Recital in that same cleanup. Worth knowing too that a Reaction-speed move (rather than Recital, which resolves too late) beats the Deathknell outright, since the target and "here" are locked when the trigger finalizes.