I don't think anyone has seriously suggested that a B 777 could operate out of BRS to the Middle East. With a runway of just 2011 metres at an elevation over 600 feet aircraft choice is limited.
The largest aircraft that BRS has seen for many years is the former First Choice B 767s of TUI. They had fewer seats than TOM's 767s and until summer 2014 operated weekly to Sanford and Cancun with the latter route requiring a fuel stop at MAN outbound. The occasional A330 has also appeared on rugby charters to Ireland.
Turkish to Istanbul has been mentioned quite a lot in the past year with anno aero and even the ubiquitous Simon Calder discussing the possibility. To plagiarise the Dickensian Micawber it's a case of waiting for something to turn up.