If you want a thicker sound, go for thicker sounding woods - mahogany etc. Not swamp ash and maple!
The bridge alone will make little difference.
I'm most likely working with a tele body, either that or an HH strat, and after all the alder in my life, I want to try a slight contrast, hence the swamp ash. Plus, I'm saving mahogany for another project in the future, one involving p-90s (I'm especially anxious to give that one a try, but it'll definitely cost way more than this one, plus the wiring will be an absolute nightmare).
I know that the bridge isn't as critical as the actual woods chosen, but they do have an effect on the sound. I read in a post somewhere that floyds thicken the sound of pickups, but given that it's a huge hunk of steel, it's to be expected. Since the guitar will be hardtail, I also know that the bridge won't affect the sound as much (since there's less bridge than with a trem), but every little bit counts!