If the device is deemed to be information technology equipment (which it may, since it uses Bluetooth) you would be under the '60950' standard - UL 60950, and if you want to cross the border into Canada, CSA C22.2 #60950 (the standards are largely identical, so it makes sense to get both).
Intertek ETL is a US Nationally Recognized Testing Laboratory (NRTL) authorized to test to UL 60950. You could use UL, CSA, TUV, MET or any other NRTL to do the approval - it doesn't have to be Intertek.
The best way to know if the product needs approval is to get an opinion/quotation from an NRTL - they'll tell you what they believe the product needs and how much a certification will cost.