The 19-time Grand Slam winner caused havoc with his backhand, leaving Bedene with little chance of creating an upset.
In the end, Federer, who stood alone for most of last season when the likes of Andy Murray and Novak Djokovic were sidelined with injuries, sealed a 6-3 6-4 6-3 victory in around one hour and 40 minutes.
The 36-year-old eased into the first set as he broke to go 3-1 up, and it was smooth sailing from there as Federer set the tone with an early break point in the second set.
Bedene struggled to get games on the board, but he did manage to save three break points, which forced his Swiss opponent to serve for the set.
The Slovenian was not as fortunate at the end of the third set as Federer broke to gain match point.