The scandal was her best weapon.
In her fear she overused the useless and potentially dangerous one for her and derused the best one
Raising scandal further and getting away from the man at the same time would also further protect her, while the umbrella thing could just enrage the guys to follow her after she gets out of the bus...
If its a gang of guys trying to do this they are more likely to be afraid by public notice and assaulting a woman everyone is seeing carefully than about a couple of umbrella hits against their bunch.
It just wasnt smart. The scandal was perfect, the extra assault on her part was plain dangerous.
You don't know she "overused" anything though. Look at how she managed to dominate the space, herd all the men toward the back of the bus, with the exit behind her, and clear space between. She ended up standing facing all the men with her "weapon" in between her and them and an escape route behind her. The position she maneuvered herself into was ideal for self defense in a situation where a large number of the men on the bus could all be perceived as a threat.
Think of the alternative, sit back down quietly and hope for the best, giving the men an opportunity to determine where they are going to position themselves and what they are going to do next.
The trouble is, you are assuming she was not at risk of any more than a little bit of uninvited fondling, so her reaction looks extreme to you. In fact, she was potentially at risk of being violently raped to death by all the men on the bus. It would have been
reasonable for her to perceive that level of risk in India and react accordingly.
Making a lot of noise and a big scene is useful for creating confusion, controlling the event and putting people exactly where you want them to be.
Which is not to say I think she was acting rationally. I think self-defense is automatic, but it's always got to be a little extreme in order to be effective - especially if you are smaller than your attacker. You don't just want to stop an attacker's behavior for a moment, you need to completely change their mind about picking you for a victim, permanently.