when can I move a camelia bush,

It's usual to move shrubs in late autumn, so that's when I would do it. Get it settled into its new home ready for its flowering time!

Make sure the new site is ready before you dig up the shrub. Move it with as much rootball as you can manage...and ask for some help from friends/neighbours as it will be heavy. Water it all year, next year, with rainwater if possible...even if it rains!