These are the steps I've used in the past on an unrooted Bionic to install updates. It contains steps you may have done already if you've connected your Bionic to your PC before.
Don't worry that the name of the file is 5.9.902. Motorola gives the name of where is coming from, not where it's going to. Be sure you have the Motorola drivers installed from USB and PC Charging Drivers - Motorola Mobility, Inc. USA on your PC. These may install automatically when you connect your Bionic to your PC.
1. On the phone go to Menu>Setting>Applications>Development and check "USB Debugging."
2. Plug phone into computer.
3. Press "Mass USB Storage" from the list of choices. Two drives will show up. One is MOT (Internal Storage) and the other is Removable Drive (SD-EXT).
4. Put the downloaded file in the root (ie main area) of SD-EXT (not Internal Storage). No need to change the name or extract it.
5. Eject both MOT and Removable Drive and disconnect the phone from your computer.
6. Power phone down
7. Boot into stock recovery (adb reboot recovery) by holding Power and Volume Up/Down at the same time.
8. Select "Recovery" by pressing Volume Down, then press Volume Up to initiate it.
9. When the robot appears, press both volume keys in at the same time.
10. Select “apply update from sdcard” using the Volume keys, then Power to initiate it.
11. Using the Volume keys, choose the file that you downloaded (above), press Power and let it load.
12. When the install is done, press Power. It'll reboot, but it'll be longer than normal (about 6 minutes)
The whole process, from moving the file into the SD-EXT card to phone rebooted is about 10 minutes. Of that, 3 minutes will be the phone extracting the files (Step 11) and 6 minutes for the install itself (Step 12). A long time to stare at your phone, I admit.