First question is how long should I leave it in the primary?
That's like asking a chef how long you should cook meat. The correct answer is "until it's done". Time can vary, so learn to recognize when it's finished. The gravity stops changing, the yeast starts to floc out, and the cider gets brighter. Could be a week or two, certainly I'd hope it is done within a month. It probably won't be bright yet; cider takes longer than beer to clear.
Will leaving it in the primary for an extended time produce any off flavors?
Possibly. You run the risk of autolysis. It's not a definite; you're dealing with probabilities. It's not a good flavor, so it's worth avoiding.
I have read that it will improve with aging.
Indeed it will, as long as nothing went off during the fermentation. I like to age them at least 6 months, but that's me. Nothing wrong with a year, certainly.
I am not in a hurry to drink it and would probably save it until next fall, but would it be better to bulk age in a secondary fermenter or age in bottles? I do not keg and was not planning to carbonate.
Then I'd bulk age it somewhere cool in a secondary. If you bottle it, it could carbonate on you if you misguessed that it was actually finished. If you bulk age it, you can also adjust it to your taste prior to serving. More options that way, as long as you have some place reasonable to store it and don't need the fermenter for something else.