First of all, are you talking about the Web Vault (logging in to vault.bitwarden.com in a regular browser tab), or the Bitwarden browser extension?
Assuming you are referring to the browser extension, which version of the extension do you have installed? Find the version by clicking on the Settings (
) icon in the bottom right corner of the browser extension window, scrolling down to the “Other” section, and clicking the About link.
If you have the current version (2024.1.0), then click on the profile icon (a colored circle with your initials) in the top right corner of the browser extension (Arrow #1 in the screen shot below), and click Log out (Arrow #1 in the screen shot below):
Finally, click the Yes button in the confirmation prompt.