In most Batman media at one point in time or another a situation arises where both Batman and Bruce Wayne need to be seen together. While this has been accomplished by both Alfred and Superman, in recent years the go to person to portray Batman in Bruce's place would be Dick Grayson, aka Nightwing. But, has this dynamic (pun intended) ever gone the other way, where both Dick and Nightwing need to be seen together with Bruce filling the black and blue (or red) tights?
Given the relationship issues between Bruce Wayne and Dick Grayson which led to the creation of Nightwing, it is very unlikely Batman would ever wear the Nightwing outfit unless specifically asked by Grayson. There are no known incidents of Bruce Wayne wearing the Nightwing outfit.
In the previous continuity where the character Nightwing was created, it was Grayson's attempt to step away from Batman's plan for him to inherit the Mantle of the Bat.
Grayson wanted a heroic identity which he could make his own allowing him to quest for justice without becoming a crazed vigilante which he (at the time) considered Batman to be, at least some of the time. It also explains his reluctance to wear the Mantle during the time when Bruce Wayne was presumed dead.
This isn't to say there couldn't be a circumstance where Wayne would wear the outfit and imitate Grayson's fighting style (because he could). In my knowledge, it just hasn't happened yet.