Can I cast a spell while another spell or ability is resolving?
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.