But have you done this recently? You signature says that your last off-property stay was in 2009. Like everything else, hotel prices have gone up. I'm not saying it will be impossible. But it will be harder than it was 3-6 years ago. And since the OP wants to be on the bus line, doing hotwire or priceline might not be a good idea.
The Motel 6 behind McD's across from Old Town isn't half bad. It's one of the few pet friendly hotels, and it was cheap 2 years ago. The Lynx bus is right outside to Disney's TTC. It's one of the first hotels along 192, so it's REALLY small compared to a standard room at a newer hotel.
I want to say they were putting in a new Lynx route along Palm Parkway, right outside DTD, and there's some decent hotels along there. But probably not under $45 a night in low season.
A couple years back, got a room at the Holiday Inn Express by I-drive for $40ish a night. It was through a name your price site, but it was also totally random which hotel I got. Although they were really nice and upgraded my aunt to a one bedroom suite with a kitchenette for free.
I just could not imagine staying offsite without a vehicle. How is the OP supposed to get into town? If she's flying, she'll have to get from the airport (although there is a Lynx bus between Disney and OIA).
The cheapest Disney option, which is the safest option, would be to pitch a tent at Ft Wilderness. It's cheap enough to get a partial hook up site, the free Magical Express, the free transportation onsite. It's easy enough to get to Sea World, but Universal is another story.