The issue with a question like this is...just about every Bay Rum soap will have a different spin on "Bay Rum" even if it is only slightly different. I have so many.
My recommendations for Bay Rum soaps/creams would be:
Captain's Choice Bay Rum (Soap or Cream) - A very true Bay Rum scent without much complexity. But definitely true to the Bay Rum scent. At first I did not care for this, but it was one of those things that won me over in time. Grows on ya.
Chiseled Face Bay Rum - An interesting take on Bay Rum that has real Rum and Lime notes.
Phoenix Artisan Accoutrements Atomic Age Bay Rum - Pride themselves on removing the clove scent. My wife is ok with Bay Rum, but this one she gives a solid thumbs up to. This is Bay Rum on steroids.
Barrister and Mann Bay Rum - In my opinion, one of the best on the market. They blend in all of the classic Bay Rum scents so well, the scent experience is just amazing...you're not sure which scent will reach out and grab you with each whiff.
Stirling Bay Rum - This is a nutmeg-heavy scented Bay Rum that's unique and wonderful. Stirling soaps often speak for themselves.
Wet Shaving Products Bay Rum - This is a Bay Rum and lime combination that is well done. I have the Formula-T version of this shave soap.
I could list others, but, in my opinion, the ones above are not only good Bay Rum scents, but also good performing soaps.
I really like the scent of the PAA Atomic Age Bay Rum - I actually just purchased it. I have the original formula, but I have to ask this forum who have used their soaps extensively - Do they seem pasty to any of you? The tub I just purchased literally loads to my brush more like a shave paste vs a nice creamy lather, is this their formula? Or am I missing something in the brush application?
From a scent standpoint - I really like this Bay Rum scent.
My favorites would include:
Stirling
Mike's
WSP