How far away is the tub from the main drain? If you're within 6' you don't need a AAV unless you have 2 fixtures behind a vent. The best way to explain that to you is...if you fill up the tub and drain it, does the sink or toilet in that room make a sucking sound?

By code, AAV's or back vents are supposed to terminate 6" above the highest fixtures flood rim on that line.

Under the IPC & IRC the maximum length of a fixture arm can be computed by dividing the diameter of the drain by the pitch. If an 1-1/2" line is installed with the code standard 1/4" per foot pitch the maximum lenght would be 1.5 / .25 = 6ft but in this instance the line has a 1/2" pitch so the maximum allowable length would be 1.5 / .5 = 3'. (The bottom of the drain line at the trap weir may not be higher than the top of the line at the vent opening).

Both the configurations illustrated above would not pass code for a number of reasons.

The simple solution would be to remove the drum trap & extend the length of the tub drain tailpiece. Code will allow up to 24" vertical drop from the tub drain opening to the water level in the trap.

Attach a P-trap and run the line with a 1/4" per foot pitch.

A wye can be installed on the drain line with the side input angling downstream. You can then put a street 1/8bend on the wye side opening input, which would turn the side opening vertical and attach an AAV where the base of the AAV is 4" above the drain line.

REF-IPC
917.4 Location. The air admittance valve shall be located a
minimum of 4 inches (102 mm) above the horizontal branch
drain or fixture drain being vented The air admittance valve shall be located within the maximum developed length permitted for the vent. The air admittance valve shall be installed a minimum of 6 inches (152 mm) above insulation materials.