The usual way is to execute:
fastboot oem unlock
But this will erase all my private data.
Unlocking the bootloader will wipe your device.
You can however get root access without unlocking the boot loader.
If you then still want to unlock the bootloader, as you already have root access you can follow Sparx's advice and use a back up app before doing so.
What if you backed up all your data using Titanium Backup / MyBackup Pro or some such app, then unlocked the bootloader and finally restored the data?
That would then leave you with (after some effort) an unlocked phone and your data.