How should I securely type a password in front of a lot of people?

Use the blanket of security, as seen in the Snowden documentary Citizenfour.
It involves placing a blanket over your head, the keyboard and monitor and typing in the password.
It will look weird but for security's sake it may be worth it.

Related post with demo pic - In CitizenFour, what was Edward Snowden mitigating with a head blanket?

You could use Two Factor Authentication that uses your phone to log in along with your password. That way, even if they see your password, they would need your phone, too to log in.

Get a password manager like KeePass and store your password there. Use the auto-type or a plugin to enter the password.

• Unlock your KeePass database when you boot your machine, so that you don't have to unlock it with people around.
• Set it up so that it locks automatically when you lock the screen (just in case)

Alternatively, you can remember the e-mail password in your browser, which has downsides compared to KeePass but will keep your password save (given enough scrutiny).