"have a bump" is correct and usable in written English.
This phrase is often used to refer to having a drink of alcohol. For example: "Let's have a bump and raise our glasses to a successful year!".
So we may have a bump from time to time.
"Why does she still have a bump?" This comment was actually made by Anna Botting, also of Sky News.
Always saying what no one is thinking, Anna Botting of Sky News asked when the Duchess of Cambridge emerged with her newborn baby: "Why does she still have a bump?" To which the whole of Twitter chorused "Because she had a baby yesterday!" Equally helpful was OK! Magazine's offering of a "post-baby weight loss regime" for Kate.
He listens to the recent history of 13 bodies: I have a bump on my head that won't go away, one woman says; I have a lump on my neck that feels like a gummy bear, a man reports; my knees hurt when I sit for too long; I get computer face from my computer; I have a freckle; a sore; a taste in my mouth; a fluttering in my chest at night after I eat ice cream.
"I didn't want to have a bump on it.
"He did have a bump on his head but in 24 hours it was gone.
