There are definitely different strategies involved in doubles (of course) but the skill sets don't vary that much between doubles and singles. In both cases you need to serve well, volley well, return well, etc. In singles, players generally come to net only when it's advantageous to do so (to finish a point after hitting an approach shot for example) whereas in doubles one player is at the net before the point even starts.
The return of serve matters a little more in doubles because you generally need to keep the ball low and return cross court, otherwise the man at the net on the opposing team can easily poach the return and hit a volley winner - so a weak return won't help your chances at winning return points/games much.
The big difference between the singles and doubles game is movement and court coverage. Singles players have to cover the entire court themselves, while doubles players really only have to cover half the court. So singles players have to run more and are generally in a little better condition than doubles players but that's just a generalization.
I think in the case of top doubles teams like the Bryan brothers, the skills they have developed and work on most are specific to doubles (like moving and covering the court together in tandem, quick volley reflexes, etc.) and since they don't focus on or play singles, they don't have the same level of skill in singles. They're still probably as good as any top 500 ranked singles player in the world but most players in the top 50 to 100 would beat them 9 times out of 10.
Most of the top singles players can play doubles pretty well (look at Jack Sock and Vasek Pospisil who teamed up for the first time and won Wimbledon this summer for example) because they've played enough doubles to know how the strategies differ from singles and all of the serve, return and volley skills are already there from their singles game. I think the biggest hurdle for doubles "specialists" would be adjusting to covering the entire court themselves and having to adjust their shot selection and strategy accordingly.