The iodine dip is an interesting idea - no idea if it would work, but I’m curious to find out.
That said, if (it’s a big if) your star’s bacterial infection is similar to Sea Star Wasting Disease (which you can decide by looking at the symptoms for it yourself) - where bacteria on the starfish’s surface actually suffocate the star an iodine dip may actually be helpful in treatment by killing off the surface bacteria and allowing the star to get oxygen again (Point Defiance Zoo and Aquarium used antibiotics successfully on their stars to cure the disease a few years back, and this would theoretically have a similar effect). Unfortunately, Google seems unable to provide me any information about other starfish illnesses and diseases right now, so this is the only one I can seem to find any info on for the moment, but if the symptoms are similar, giving the star a somewhat cooler (probably ~75F vs most tanks being kept at 77-78F), low nutrient environment with high oxygenation after the iodine dip could potentially help with recovery, as the bacterial species that cause SSWD are copiotrophic (they like high nutrients), so the cooler water and low nutrients would slow bacterial growth while the oxygen helps the star recover from suffocating. The cooler temp might also slow the star’s healing though (many marine organisms grow more slowly in cooler temperatures), so that is something to consider before trying any of the above potential advice.
Beyond that, from what I’ve heard, depending on conditions and the individual species, a healthy sea star should be able to start recovering from serious injuries (like lesions or lost limbs) within ~3 months. Depending on severity and water quality, though, I’d guess a timeframe of ~6-9 months wouldn’t be too unrealistic.
SSWD or not, though, let us know what you end up doing for treatment and how it goes. I really am curious if the iodine would help or not.
Also, out of curiosity, what is your starfish? I saw one of the comments mention a sand sifter, but I don’t see any specifics in your post.