How can I switch fire mode in Call of Duty Modern Warfare Remastered?

I've tried several weapons with B, and nothing happens

The default button is B.

Gaining Complete Control

When using a keyboard and mouse in Modern Warfare on default settings, these are the keybinds that have the following basic commands (these commands can be all be re-bound to keys within the Settings menu):

...

B – Alternate Fire: Utilizing this function when using a weapon that offers multiple firing modes – i.e. an Assault Rifle that has both fully-automatic and burst fire modes – changes the fire mode of that weapon.

- "GETTING STARTED IN MODERN WARFARE®: CONTROLS AND SETTINGS (PC)" @ blog.activision.com

As others have said, if B does not work, I would double check key bindings.

Failing that, I would make sure the weapon actually has alternate firing modes.

Failing that, I would double check your B button works; I suspect it must if you successfully used the character in the question.

Failing that, I would reach out to the Activision technical support team.