I have to agree with those who say oiling the entire bracelet is a bad idea. Those hollow links will most certainly ooze oil for months....no matter if you wash afterwards with dawn. To compare to gen -- Rolex doesn't lubricate their bracelets. Part of the precision of the $1000 bracelet is the fact that all of the surfaces are smooth and precisely fit together to give a smooth feeling. That can't be replicated just with lubricant. Additionally, lubricant picks up dust and dirt and turns it into grinding paste that after a year or so results in a lot of "stretch". I think the best method is a hybrid of what is mentioned here and in responses.
first, use an ultrasonic cleaner --- make sure to utilize a cleaning agent! Use the ultrasonic for several cycles....I try to make sure that 45 minutes or so of run time has been used. Also -- take the bracelet apart. All screws should be taken out of links and cleaned. To prevent scratches during cleaning from the vibrating action, space out the parts or do them in batches. One last tip is to use hot water in the cleaner.
second, rinse the bracelet parts with water and dry off with a microfiber cloth. You can also use a hairdryer if you think there is water inside the chain links. You're going to these lengths so do a thorough job drying. This is stain"less" meaning it will still rust if given the right conditions, just less than other steels.
Then, loctite the ends of each screw and let dry. Don't get extra locktite on the barrel of the screws otherwise you've just replaced all the stuff you cleaned off with a new bit of grime.
then, identify any links or parts that are still stiff. Only those parts should be treated with the smallest amount of DRY CHAIN LUBE. Ex: WHITE LIGHTENING. it's true this stuff is toxic but it's a necessary for true Gen like feeling because even after ultrasonic cleaning, we can't expect every bracelet part to be manufactured to the exacting specs of gen Rolex and then hand polished and inspected under microscope. There will inevitably be some tight spots. When using the dry chain lube, use a needle to drop on an even smaller amount then a full drop. Once it sits for a few minutes in the joint, work the tight part around and then rub off the exposed joint with a cloth with alcohol on it. Then use a damp cloth and the microfiber to polish.
nice thing about the dry lube is it doesn't pickup the grit...and will last for about six months in something like a watch bracelet that isn't exposed to the elements that bike chain would be.
all of this should be followed up with genlike maintenance. Rolex advises owners to wash the watch off with dawn everyday when washing hands. Just wash it and rinse like you're washing hands. Will keep your piece beautiful for years.
hope this helps adds to the debate! It's just my 2cents but a tried and true method.