For single addresses I just email myself the link, open the email in the mail app and click the link.

To get the full set of bookmarks and history from desktop Firefox requires using Sync. https://support.mozilla.org/en-US/kb/how-do-i-set-up-firefox-sync

If you are clicking links in Facebook, Twitter or Email apps on the phoe and not being offered to choose which browser you will need to unset the default browser.

This is a bit tricky.

• Go to the Android home screen
• Open the settings
  • press the menu button and select settings on most phones
  • on phones without a menu button go to all apps and select the settings app
• Open the Apps or Applications setting item
• Select the all tab
• Find the default browser
  • this is tricky as it has different names depending on the phone check for
  • Browser
  • Internet
  • other 3rd party browsers
• tap on the browser item
• tap on clear default or uncheck it
• If the button is greyed out or not checked then try a different browser in the Manage Application settings

Once cleared you can set a new default by clicking a link in email or other app then checking the always use as default, then selecting Firefox.

Thanks kbrosnan, after clearing the defaults, it now opens seamlessly.