Should I buy a seperate dac?

It depends on the rest of your system. I didn't see a virtual system under your user ID. 

Your CD player has Optical and coax out. Typically, if you had USB out you would try both and see if one sounded better. 

Schiit is a good bet in this range of the market. Higher up is almost always better... but what the rest of your system is could be limiting... or not. 

My experience with outboard DACs goes back to the mid to late ’90s so I don’t know if it would be applicable to the digital of today, but back then I did find that adding digital separates between my $600 Carver CDP and my preamp improved the presentation.

A few years ago I decided it was time to upgrade my ancient front end, so I bought Marantz SA10 because I wanted to do the SACD experience and I also wanted to get away from separate boxes and the cabling that goes with them.

Make sure it’s the BiFrost 2 and not the original Bifrost. The 2 is hands down much much better than the original!

Save your money.

For a first time DAC, I would recommend one above 2K. Any less, one will always want something better up the line, eventually.

Ultimately, yes.