Depends what it is and unsure what you mean by "bloom", is that actually a stain of some kind?
The best method if you can get it in a a ROS with Abranet mesh disks.
You need first to decide what level of finish you had or want as the grits you go down to will determine what you get. On Mistral or Corian for example you can get a nice satin with 400g or glossier with 600g and above.
Can easily be done by hand though if not a big area, just more work.
Whatever you do it will need a final polish and the manufacturers sell a care kit but most hard surface polishes will do the job.
Rather than explain in detail I suggest you do some googling as there are instruction videos out there. Most of the worktops I installed were Mistral but the principle is the same.
Here's a generic video but do a search there are loads of how to repair and finish these products.
https://www.youtube.com/watch?v=_xiVtgcHOtE
EDIT:
I glued some bits together recently, turned a lidded pot and polished using some car G3 compound witch worked beautifully and gave a gloss finish might be worth a try if you have something similar though likely just as expensive as worktop polish if you need to buy.