Grab bars are only as safe as what they are mounted into, so removing and reinstalling them correctly matters as much as the move itself. Note the stud or anchor method now so the new bathroom gets the same secure mounting.
Pro tip: If the bars were professionally installed, ask the same installer or a handyman to reinstall at the new home; they will know the correct height and angle for the person who relies on them.
Watch out: Grab bars must be remounted into a stud or a properly rated anchor at the new home; a bar mounted into drywall alone can pull free under body weight and cause a fall.