Our h cars are suppose to be good for towing 1,000 pounds. So your bike and a trailer should not exceed that weight.
But, you might want to keep it in "drive", not overdrive. Yes, gas mileage may suffer.
If you are on very level roads, it might be safe to use OD, but do not go up any grades in OD while towing anything.
Reason - "drive", when it hits that gear, is a straight connection from input to output (in a sense) but with OD, the gears are having to work to provide the .7:1 ratio for OD.
Drive is a 1:1.
Now about the best hitch/trailer, i do not know.
1999 LeSabre, 3800 series II engine.