You should still be able to access BIOS with the external monitor. Are you sure it isn't set up to use "Fast Startup"? If so that could be your problem and you would need to change that.
To Turn On or Off Fast Startup in System Settings
1. Go to 'Control Panel' and click on the "Power Options icon".
2. Click "Choose what the power buttons do" on the left side.
3. Click "Change settings that are currently unavailable".
4. If prompted by UAC (User Account Control), click "Yes".
5. Do step 6 or step 7 below for what you would like to do.
6. To Turn On Fast Startup.
6a. Under "Shutdown settings", check the "Turn on fast startup box", click "Save changes", and go to step 8 below.
7. To Turn Off Fast Startup.
7a. Under "Shutdown settings", uncheck the "Turn on fast startup box", click "Save changes", and go to step 8 below.
8. You can now close the 'System Settings' window.
Note: If the "Turn on fast startup" setting is not listed, then you will need to close the "System Settings" window, enable "hibernate", and then start over at step 1 again.