The mystery of Amy's disappearance is compelling because there are so many theories/possibilities. Personally, I believe that one of two things happened to cause her disappearance:
Theory #1: Amy accidentally fell overboard.
Amy was last spotted lounging on her balcony around 5:30 am, and mysteriously gone 30 minutes later. She was nowhere to be found on the ship by her dad, who immediately started looking for Amy before passengers started to disembark. Her sandals were left behind on the balcony, and a table was pushed up against the railing. According to Brad, Amy was tipsy and feeling unwell when he last spoke to her earlier that morning. The simplest explanation is that Amy was hungover, and she felt the urge to puke and started to make her way into her family's cabin to use the toilet (hence the slider partially opened), but then realized she wouldn't make it to the bathroom in time, so instead, climbed on the table, leaned over the railing, lost her balance and plunged into the sea. The unknown noise that woke her dad was the commotion of Amy going overboard.
I do not believe that Amy committed suicide. She had no known history of suicidal ideation, and no note was left behind. I do not feel that the 'message in the bottle' was a suicide note but rather a love letter. If anything, it showed that Amy had a high level of self-awareness, and was willing to take accountability for her actions. Rather than holding in her feelings, she expressed them to a trusted friend. Amy 'came out' to her parents in 1995. She disappeared in 1998. That's a lot of time for her family to gain acceptance. Her family was adamant that they loved her unconditionally, even if they were initially shocked and disappointed. I do not think that Amy's sexual orientation had anything to do with her disappearance.
Amy had a lot of positive things going for her around the time she vanished. She had gotten a place of her own, a dog, and a new job. Amy cherished her Miata. She had a solid network of friends, had patched up a relationship with an ex-girlfriend, was athletic, and had hobbies (such as photography) that she was involved with, even on the cruise. From both the videos, and Amy's family reports, she was having a good time on the cruise. The post card she sent home to a friend seemed to confirm this. None of this fits with suicide.
Theory #2: Amy met with foul play on the ship.
There were lots of suspicious incidents on the ship leading up to Amy's disappearance. Amy's family reported that the wait staff was being unusually attentive to Amy, and she is on video dancing with a member of the band (Yellow) after the formal. Amy's photo from the formal was missing from the gallery, suggesting someone outside of her family had taken it, which is weird. Reportedly, Amy had earlier been invited to go with crew members to Carlos and Charlies, but she refused. Why was someone trying to get her off the ship? Amy's mom reported an unidentified man staring at Amy. And Amy told Brad, when returning to their balcony after a night of partying, something to the effect that she was being hit on by a crew member but she brushed it off.
It has been theorized that Amy snuck off the ship to buy drugs; personally I'm more inclined to believe that she was lured into someone's room or an unauthorized part of the ship with the promise of something (some people suggest drugs, although it has never been established that Amy was into anything stronger than alcohol and tobacco). Amy and Brad separated at the tail end of their night of partying, so its possible Amy could have made plans with someone that Brad was unaware of. Maybe she lied to Brad about feeling unwell, using that as an excuse to stay out on the balcony instead of going to bed because she didn't want to fall asleep and risk missing a meeting. Somewhere in between 5:30 am and 6:00 am Amy grabs her cigarettes and re-enters the cabin through the slider (purposely leaving it open so the white noise of the sea masks her movements), slips on one of many 'unknown' pairs of shoes she brought, and quietly exits the cabin. Amy is then spotted by a witness (a young guest) in a glass elevator with Yellow heading up to the closed disco, supposedly (but unproved) within the time frame she went missing. A short time later the same witness observes Yellow on the deck but does not see Amy. Where did she go? Perhaps wherever she was lured to, someone made a sexual advance towards her and she resisted, resulting in her death. Her body was concealed in luggage, and removed from the ship at port in Curacao.
I favor the theory of foul play over sex trafficking because I've seen no evidence to support the assertation that the ship's crew was running an elaborate sex trafficking ring. If they were, there should have been many more mysterious cases of missing women before and after Amy Bradley. Besides, Amy was not a likely target. She was a well-educated, financially-secure, adult woman travelling in the company of her parents and brother. I didn't find any of the various sightings on the island credible.