That adapter is "rated for 5000 pounds" which means total towed weight, not tongue weight. Your trailer, a 2018 Bullet Premier 22RBPR has a "shipping weight" of 4972, which is without a battery, spare tire, no optional equipment and empty propane tanks. There's no way possible to stay under that "magical 5000 pound limit" with only 28 pounds remaining in trailer weight. That doesn't include the weight of your hitch, the bike rack or the bikes. Then add the above items (propane, battery, spare, etc) plus your camping equipment and supplies and it's even further from a realistic means to add bikes and a bike rack to the mix...
Just using a 2" sleeve in a 2/5" hitch receiver reduces the weight capacity by nearly 50%. Mounting your hitch 10-15 inches behind the actual receiver is "physics nightmare" !!! Don't attempt it without discussing it with a "towing expert" but my "amateur towing experience" screams "run the other way" !!!!!
No, it's a bad idea to even attempt such a feat... If you look at any "towing information site" they all warn against using any type of hitch extension with a weight distribution hitch system....
You'd be much better of, assuming you have some tongue weight allowance after hitching your trailer to the truck, to consider a rack to mount over the propane tanks and install the bike rack there... Here's one type of such rack:
https://www.etrailer.com/RV-and-Camp...gaAsOfEALw_wcB
ADDED: The only hitch extender that doesn't significantly reduce the receiver capacity is a Titan extender, designed to be inserted into a 2.5" receiver and used with a 2" WD hitch. It doesn't have any means to "attach a bike rack" and is only intended for use on rigs such as a long cab-over camper to extend the towing capability to the rear of the camper overhang so you can tow a light boat or trailer with an ATV, etc. You can view the e-trailer response to using a hitch extender and see the Titan system here:
https://www.etrailer.com/question-78216.html