Arrogant, Immature Trolling Ass Wipe
Bring it with you, ask if it'd be alright to hook it up when no one else is using the tv. Pretty simple. That way you're respecting her authority and not overstepping your bounds. 37 is fairly young, so I'm sure she at least has a passing familiarity with video games, and won't think you hooking it up means her tv is broken or going to explode.
Originally Posted by ronin_the_great
Is it an apartment or a house? Sounds like a house by your description, but just try to avoid being too loud at odd hours, so you aren't bothering her neighbors either. If it was an apartment, even more so.
Like everyone else has said, just don't be a slob and offer to help out with chores and whatnot, if you can cook that might be appreciated too since you could be working on stuff for when people get home. It kinda sucks having to do more work in the form of cooking after a long day, so that would be pretty thoughtful if you have any culinary skill.