How do you copy text from Firefox in Windows to bash shell in Unix?

If you connect to unix using putty, copy the text from the browser, then right click on the putty window to paste.

You could use Synergy to share your clipboard between the two machines.

I routinely run x2vnc from a Linux box, and have a VNC server (RealVNC) running on a Windows box. This lets me share one mouse and keyboard across the two machines, and the clipboard is also shared across the machines.