What you need is not an amp. You need a Bluetooth transmitter.
If your source is a pc, why not just buy a Bluetooth adapter for it? You are just taking an unnecessarily long path by converting it to analog and then back to digital. Is this a work machine or something where you can't install bluetooth?
yes, a bluetooth transmitter is required.
There's no conversion to analog then back to digital.
Devices like Fiio BTA30 can be plugged in USB port, Once configured in DAC mode, digital signal is converted to analog by device itself and then transmitted over bluetooth to earphones etc.
Audio quality wise, any cheapo bt 4.0 or above dongle is going to give you vastly superior audio quality to even the world's best dac hooked up to the World's best bt transmitter.
Undoubtedly a cheapo bt 4 device may sound good and serve the purpose but you get what you pay for.
Costly devices looks premium and are feature rich supporting all those codecs like aptx, aptx-HD, LDAC etc.
A 300rs dongle can't be compared with devices like, Fiio M5, Fiio BTA30 or some similar devices from Shanling and other brands.
Pcie/m.2 solution as suggested by titokhan is also better than cheap dongles, though it will only provide basic BT connectivity and can't use LDAC etc.
but at the same time it can be used to connect other BT device also like some BT keyboards, controllers etc.
BT on windows supports APTX only, so if you want something like APTX-HD or LDAC a good transmitter is required.