I had no idea what trolley bags or wheelie bags were until Google Images showed me!
Apparently, they refer to wheeled luggage.
Nowadays almost everything in the U.S., from carry-ons to large suitcases, seems to come with wheels.
For that reason, I think it may be more common to refer to the type or style of wheels.
The original style is sometimes referred to as rolling luggage while the newer style with multi-directional wheels is called spinner luggage.
EDIT: Despite the following statement found on Wikipedia, I have never heard a wheeled bag called a "roll along."
Some suitcases that include a telescopic handle and wheels are known as trolley cases (UK) or a roll along (US).
Rolling to me sounds like rolling down a hill. I prefer "roll along" when it comes to "rolling" but I haven't seen it in writing anywhere. "Wheelie bags" sounds familiar but -- is it just me? -- the form suggests British English usage.
You didn't mention why you want to know the AE term (communicating with an AE speaker, teaching non-native English speakers AE vocabulary, etc.).
If you are shopping for such a bag in the U.S. or describing such a bag that you have lost, you could just say:
a bag/a suitcase/luggage with wheels
However, wheeled luggage has been available in the U.S. for over forty years and is now pretty much the norm.
Most suitcases sold in the U.S. come with wheels and a telescoping handle so it really is not usually necessary to specify this.
Like it or not, "rolling" is the word that was and sometimes still is used by stores to describe such luggage.
Other terms used include "wheeled" and "spinner."
My personal experience has been that individual AE speakers just say bag/suitcase/luggage (without the "rolling," "wheeled," "spinner").