Bullock has been heavily linked to City with talk he could be signing a few weeks ago. He is an attacking midfielder but York City have been playing him as a striker.
The transfer window does not affect transfers between Nationwide League clubs. Reports in January said that he would come to Cardiff for an initial £75,000 with the deal worth as much as £150,000.
Bullock has played 31 games for York this season and has scored 6 goals.
York City boss Chris Brass said: "He's gone there to train with them this week. It gives the lad an opportunity to impress and everybody knows that they are interested.
"It will give Lennie Lawrence a closer look at him and Lee the chance to look at their set-up. I have said before we would never stand in his way so, fingers crossed, he does well. I don't think he will be playing for their reserves and he is due back here on Thursday."
It's reported from York that international clearance issues may see him miss tomorrow's reserve game against Swindon, that's not 100% confirmed.