Updated
There are currently 1 1 bedroom private landlord apartment rentals on HotPads in 81004.
Set the bedroom filter to 1, then open the "All filters" tab and select "For rent by owner" under "Additional options". Select "Save search" to get an alert when a new match comes on the market in 81004.
FRBO is an acronym for "For Rent by Owner." This means that the private landlord acts as the property manager and is the individual that a renter would work with directly for renting their apartment.