If he had access to guns over a long period, it would be tempting for him to use it on a woman. Which would be an escalation from his previous abuse.
He couldn't use it on someone he knew, as there would be a connection. He could use it on a stranger but probably had less motivation to do that.
Jill Dando was someone he knew of & lived near him, but who he had no connection with. An attractive woman the likes of which he would never have any chance of being romantic with. A woman who helps catch criminals such as him.
If he was going to use a gun once on a woman, having the whole world talk about it, would have been too much of a temptation to resist.