The Tools > Burn Bootloader operation sets the fuses according to the Nano hardware definition and then flashes the bootloader file to the microcontroller. It sounds like now you want to upload. The standard way to do this is via a TTL serial communication with the microcontroller. That's the purpose of the bootloader. So usually you would connect a USB to serial adapter module or cable to your ATmega328P as shown in the "Programming a sketch" section of this tutorial:
If you don't have a USB to serial adapter then the other option is to use your Arduino as ISP programmer to upload to the ATmega328P. You can do that via the Sketch > Upload Using Programmer menu or by holding shift while you click the Upload button. Note that when you do an Upload Using Programmer it erases the bootloader so if you want to later do uploads over serial you will first need to repeat the Tools > Burn Bootloader process.