My opponent has a Sorin, Lord of Innistrad with scads of loyalty. I've got a Gideon Jura and a Nihil Spellbomb on the battlefield.
He activates Sorin's "ultimate" ability, targeting Gideon.
-6: Destroy up to three target creatures and/or other planeswalkers. Return each card put into a graveyard this way to the battlefield under your control.
Is there any way I can use the Spellbomb to prevent my opponent from stealing Gideon after he is sent to my graveyard?
No. Except for effects that specifically instruct a player to cast a spell, spells/abilities may not normally be played during the resolution of a spell or ability. Since Sorin's ability is both destroying, and returning Gideon, there is no point at which you would have priority to activate the Nihilism Spellbomb to remove the Planeswalker.
You may want to read up on how priority works.
608.2f If an effect gives a player the option to pay mana, he or she may activate mana abilities before taking that action. If an effect specifically instructs or allows a player to cast a spell during resolution, he or she does so by putting that spell on top of the stack, then continuing to cast it by following the steps in rules 601.2a–h, except no player receives priority after it's cast. The currently resolving spell or ability then continues to resolve, which may include casting other spells this way. No other spells can normally be cast and no other abilities can normally be activated during resolution.
As @user1873 said, the situation you described wouldn't help you much.
One thing that would keep your opponent's grubby little paws off of your stuff, however, would be things that prevent stuff from hitting the graveyard in the first place. Any replacement effects that say something like "If a creature would be put into the graveyard, exile it instead" would keep things from hitting the graveyard and hence prevent them from being returned to the battlefield under the opponent's control (since it never goes to the graveyard due to the replacement effect).
Some examples of this include: Samurai of the Pale Curtain, Yawgmoth Agenda, and Yawgmoth Will (though this is a sorcery, and so wouldn't help in this situation).
