In Oblivion I remember being able to cast spells while wielding a bow. Very useful for healing spells and night eyes. In Skyrim though either I'm missing something, or do I have to equip a single handed weapon first before I can cast?
No, when you wield a bow it occupies both hands so you cannot equip a spell at the same time.
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.