AWS Lightsail - Accessing a mysql database in a different account?

I have 2 accounts (root user) set up. They are in the same region.

One account (call it 'Account A') has a mysql database instance with multiple database schemas.

The other account (call it 'Account B') has the webserver (we have an external developer building the web site which accesses the database schema).

I have tried doing a simple mysql connection (using the mysql client on the ubuntu server) try and access Account A's database. However, I get an 'access denied'. I have a feeling it may be because the database isn't open to the public. Is there anyway to do this securely?

Has anybody done this successfully?

Many Thanks for any help!