What is wrong with the Bifrost?
To be fair, my personal experience is that an amp like the 3A deserves a decent DAC. And the said thing is, most decent DACs are around 1K, or that's where they start. I am not too keen on delta/sigma anymore, but the RME-ADI2 is a decent one from those, or the Qutest is a good DAC too, but I personally think the Cyan 2 is way better than both.
The A6 is a fantastic streamer, and it is worth its price for being a streamer only, but the internal DAC is really not that good. It is ok, and perhaps good enough to survive on it for a few months until you save up, but the DAC part of it is like any $300 d/s DAC. A bit flat and nothing special. As a streamer the A6 beats twice as expensive standalone streamers though.
I think you could be fine with either the Bifrost or the built in DAC of the A6 for a short time, until you are able to get something I mentioned above. Pegasus and Ares II are good too, but IMO the Cyan 2 beats them all and not just by a small margin. It is worth browsing the classifieds for better prices. Just my 2C.