I'm trying out Bitwarden after moving to a Sony phone (my Samsungs came with their inbuilt password manager) however it keeps asking for a master password all the time. Is that normal?
Yes, requiring authentication regularly is the default. If you use biometric (fingerprint, etc) this is considerably less burdensome. you can adjust all this in the settings though and use whatever fits you best.
You can change that in the bitwarden settings. I have mine set to unlock with a fingerprint (fallback is a pin), and it stays unlocked for 15 mins before required the print/pin again.