It could be so many different things, but or course it's our nature to jump to the worst scenario... bear in mind that it might be nothing more than a little bit of ear moisture or a yeast infection bothering (her?)... Sometimes when dogs get a slight tickle sensation in their ear they shake it very gently-which look like they aren't sure or aware of what they're doing... If her ears smell off or feel damp and wet inside that could be all it is..... BUT it does sound a lot like "idiopathic head bobbing syndrome", seen most commonly in bulldogs, dobermans and boxers... The head bobbing can be either up and down or side to side; usually activity, such as concentrating on food or a toy, makes it go away but not always. The good news is that it absolutely does not harm the dog, and doesn't seem to not bother them at all, but it is very distressing for the owner.
Others probabilities are "Paroxysmal Dyskinesia" and "Head Tremors" which are two other movement disorders fairly commonly seen in bulldogs... If she's having a petite mal seizure- she might exhibit these symptoms but usually the dog is a bit unfocused afterwards.. Seems out of it.
Here's a site with some good info.