I was standing at the gate of white run with no persons in sight so I cast detect life and noticed one or two guards patroling whiterun. I then entered the bannered mare and as I had detect life equipped used it to see how many people were about. I noticed a greater increase of skill in the puclic place.

Ya, that fact is pact of Skyrim's wiki, the UESP (Unofficial Elder Scrolls Pages).

Even better than that: use telekinesis with one hand (to hold a potion in the air) while you use detect life in the other (the Riften market place is very good for that, by the way).

does it raise exp every time you cast of just a set amount for the duration?

it's a concentration spell. Meaning it is held for a duration, the longer it is active the more the skill increase

So when you use it, try to equip items that reduce Alteration magicka required or increase your magicka. (Bonus for both).
Use it until you are out of magicka, then wait an hour (in game, not in real life) and do it again.

Even better than that: Cast paralysis on Ancano.