So, what does one call a person that intentionally kills OTHERS as well as themselves? Since there is only 1 self, and multiple 'others', it would appear that HOMICIDE bomber more accurately fits the bill.
By the way, Timmy was not tried for homicide. He was tried and executed for Murder in the First Degree. Homicide is not a crime (except maybe in the ICC, and then only if the liberals want it to be).
"Homicide bomber" is just a ridiculous pleonasm, given it's understood that the purpose of the bombing is to murder innocent people. In the annals of normal criminality, from time to time there are cases in which someone kills his spouse or family and then himself. These are referred to as "murder suicides". So, I suppose you could call a suicide bombing a "murder suicide using explosives", but that's a trifle clumsy. Consider Richard Reid, generally known as the fortunately incompetent "shoe bomber". He was also an attempted suicide bomber and an attempted murderer. But "shoe bomber" gets the whole concept across much more succinctly. The other terms all require extra description.
Note also that the sand nazis don't call them suicide bombers. Rather, they salute them as martyrs. After all, suicide is a sin in Islam. But the Islamofascist mullahs have managed to spin their deaths as martyrdom, a heroic cost of waging war against the infidels, to be rewarded with the 72 virgins, etc.
Dumbing the language down to suit political tastes is an activity best left to liberals and worse.