An Electric/Bug is an awesome idea. Sure, there's the whole SR weakness, but then people might actually start using Spinners again. :D
Electric/Dragon would immediately be seen as an offensive Pokemon, because its two weaknesses (Dragon and Ice) are really common attacking types because of the fact that there are so many dragons and dragon counters. As for Electric/Bug, you have Fire and Rock. Fire is common, but Rock is only common in the form of SR. Offensively, there isn't much there, but defensively, there is so much opportunity. I think a defensive Pokemon with 2 weaknesses should be able to get around a 25% SR weakness, if you count Leftovers and whatever the Ability is.
A while back in French class, I created an Electric/Bug Pokemon. It was totally broken, though.