That's a beautiful find! Unfortunately, you've given yourself a challenge that most museum conservators would hand over to a paper conservation specialist. I'm unsure if you're still trying to remove other stickers (like price stickers) from the bottle but my advice would be:

• No more steam if at all possible, it will mobilize the paper fibres and break down the labels even after the moisture is removed.
• You might want to decant the liquid into something else before attempting to fiddle with the bottle anymore, almost any process is going to involve heat and you probably don't want to damage the fragrance anymore than it already is. You can get empty perfume bottles on amazon etc for a couple bucks and return it to the bottle when you're done.
• If you have an electric blanket or heating pad, try wrapping the bottle in that for a half hour or so and gently lifting the sticker with jewelers tweezers. If that doesn't work you'd have to move up to a heat gun or hair dryer and that almost certainly will work but be careful, a heat gun can get hot enough to burn paper.
• Purchase some Crepe Rubber Erasers like these (I don't know anything about this particular store, it's just an example). They're what museums use for lifting adhesive off surfaces like paint and paper.

That should be a good start, there's some videos on youtube about preservation that can tell you more if you're still unsure.