He expects to return to action next month according to the BBC's website, but the Heineken Cup tie at Twickenham on Saturday, 6 April may come too soon for him.
"The knee is coming along well. Hopefully, I'll be back within the next four or five weeks," said Bowe. "I'm 12 weeks post-operation at this stage and it's meant to be a 16-week recovery period.
"To miss out on the Six Nations and to have not been playing for the last couple of months makes it very difficult. I'm just aiming to get back on to the pitch and hopefully to play well enough to push myself back into the Ulster team again. With Andrew Trimble and Craig Gilroy playing so well, that isn't going to be easy. But if I could get myself back playing well, who knows what could happens."
Bowe is among a number of Ulster players in line to return to action after injury over the coming weeks.These include the likes of Johann Muller, Nick Williams and Chris Henry, and Bowe believes that the Irish province can challenge for this season's major honours, despite the team's recent struggles, if they can get people "out of the gym and on to the pitch again".
Last season's beaten Heineken Cup finalists take on Saracens in the last eight in a game which could set a new tournament attendance record for a UK quarter-final. The current record of 37,881 was established for the 2012 quarter-final between Edinburgh Rugby and Toulouse at Murrayfield.