The only word I can think of which combines in this way for time is 'spell' - a spell of time. It's quite old-fashioned and not used much as a partitive. It's used more as a noun on its own e.g. 'I went there for a short spell' or 'We're having a cold spell at the moment'. Otherwise, 'bit' works: 'I spent a bit of time talking with the students.'

Aside from standard quantifiers(some, much, a bit, a little), I'm not sure of what partitive I would use for time. "A bit of time" is certainly acceptable but not "a pinch of time." The only thing I can think of would be to say "A length of time.", though calling this a partitive would definitely be a stretch. "We will be away from each other for only a short length of time." Partiality in English is easily shown through our quantifiers and adjectives because we don't really have a robust count-word system or partitive case. Hope this helps :)