Can you cast a spell with a bow equipped?
Solution 1:
No, when you wield a bow it occupies both hands so you cannot equip a spell at the same time.
Solution 2:
You can't.
The bow is counted as a 'two handed' weapon (but not for skill) so you can't cast a spell while doing it.
This differs from Oblivion as in that game you don't put items in use against 'hands' per se, so you can cast a spell while wielding your bow.