There are several reasons why a cat might meow repeatedly at night wanting to come into the bedroom. Here are some common reasons:
Seeking attention: Cats are social animals and enjoy human companionship and interaction. If a cat feels lonely or bored at night, it may meow and try to get into the bedroom to attract its owner's attention.
Habit Formation: If a cat has always been allowed into the bedroom, it may develop a habit of considering the bedroom its territory. When it is confined outside the bedroom, it will meow to demand entry.

Comfort needs: Some cats like to sleep in warm places, and if the bedroom is warm, they may meow to ask to enter the bedroom.
Need for security: If a cat feels insecure or scared, it may also meow and want to come into the bedroom.
Physiological needs: Cats may need to use the litter box or drink water, which may cause them to meow and ask to enter the bedroom.
Health problems: If a cat is in discomfort or pain, it may also express this through vocalizations.