With jellyfish swarming our Wellington beaches, I've swotted up on treatments. The same treatment applies to Mauve Stinger Jellyfish and Blue Bottles, so you don't need to work out which one stung you.
Don't apply vinegar. This will just cause more stingers to fire!
1. Remove any tentacles (eg. using towel to avoid secondary stings)
2. Wash in sea water
3. Soak in warm water (45 degrees C) for 20 minutes
BTW, the Blue Bottle is not a true jellyfish but a siphonophore, which differs from jellyfish in that it is not actually a single creature, but a colonial organism made up of many minute individuals called zooids. (http://en.wikipedia.org/wiki/Portuguese_Man_o%27_War