Start with some basics.
You must have a trap in the line from the sink to the sewer pipe to block sewer odors.
A trap means you need a vent "before" the trap so waste will flow reasonably well through the trap.
Since many (not all) RV Park sewer ports are elevated above the surrounding grade (to prevent surface runoff groundwater infiltration into the sewer), and since any 3" sewer cap and adapter to "garden hose" (or similar) will increase that height, you will also have a "secondary, unintentional" trap where water accumulates in the hose where the hose lays on the ground. This secondary trap may cause slow or blocked drain. In this situation, most stinky slinkies require a bridging
device like this one from Camco. This keeps the hose high enough for gravity feed to the drain rather than "trapping" effluent in a saggin hose that's lower than the sewer input pipe.
Sometimes you get lucky and you're drain outlet will be just a few feet from the RV park sewer pipe, but often the run is 15 to 20 feet. Even your "garden hose" would benefit from resting on a sewer hose support.
There are some good adaptations for Pop-Up (PUP) drains that incorporporate a vent and a trap. See forum threads for designs. If your PUP does not have a trap, again you need one to keep the main sewer odor out of your camper. (PUPs dumping into a 'bucket' or jug don't have this problem, so many don't have traps.) If it does have a trap, the trap will function far better if it also incorporates an
"instavent" vent like this one. Do NOT make the mistake of a simple, open vent like the one at your home (thru the roof), because sewer gasses will collect on the road side of your camper, and it will stink to high heavens. If you don't have a vent and trap on your PUP, you can incorporate both outside the rig.
This or something like this is all you need to connect your "garden hose" to the sewer line. There are several choices for this fitting.
Last thing: As soon as you hookup to the sewer, run some water down the drain to fill the trap. A "dry trap" does nothing to stop the smell from filling your rig.
That seems like a whole lot of trouble to avoid dumping a "bucket" now and then, but it can be done.
P.S. Perhaps part of the issue is the 15 gallon bucket or jug. 15 gallons of water weigh almost 125 pounds. Even 10 gallons of water come to 83 pounds. That's a hefty lug. A 5 to 7 gallon jug should be enough. Most big RVs are not generating 15 gallons of grey water per day (yes, some do, but most don't).
P.P.S Beating a dead horse. I have
one of these for blackwater when I am boondocking where there are vault toilets. This 15 gallon container has wheels and it has all the fittings necessary to connect to a blackwater dump on an RV site. Just sayin'. Perhaps that's what you have already??