I was able to transfer my Nikon D3400 photos to the smartphone using SnapBridge. Can I also transfer photos using Bluetooth to the PC? Or can I only doing it using an USB cable or the SD card?
No you'll need to use the USB Cable or SD Card as you guessed. You can review all the features of SnapBridge on Nikon's site: http://nikonimglib.com/snbr/onlinehelp/en/index.html
In theory there's no reason why Nikon couldn't come up with an app for Windows/Mac to do the same thing as is done to the smart device but so far they have no put anything out to do that.
A good loophole is to download it on the mobile device and then back them up with Google photos, and then just hop on a computer and sign into your Google account. Bam.