There are 2 types of account selectors in Mailbird. The first is hidden and the second is always expanded.
This is the first one.
In the hidden account selector type, Mailbird will only show your selected account. If you want to access the other accounts, hover over your selected account, and your other accounts will show below your selected account.
The second setting keeps all accounts expanded, you can change this from Settings > Accounts, then check/uncheck “Always expand account switcher”
By checking the option to “Always expand account switcher”, you no longer need to hover over the active account to see all other email accounts. All of your accounts will be displayed by default.