Bumping into people at softplay is to be expected.
At other places that are busy and crowded, it is your responsibility to keep them close by - usually by holding their hand. Presumably it was dark ig you were at a light show and he had a glow stick? He should be close by your side at all times then. Especially in a busy place. That is your responsibility, not his.
So, you get his attention beforehand and explain your expectations to him. You explain to him that it can hurt people if he bumps into them. Most children don't want to hurt other people instinctively. You explain to him that, if he bumps into someone, he has to say, "I'm sorry,' and explain to him what that means; why people say it.
You explain the consequence to not meeting your expectations. Eg, if he runs around and bumps into someone and doesn't say sorry, then you will take him somewhere to sit and calm down or go home. And you stick to it.
You don't use a place being busy as a reason for not doing so.
thanks for that, the lady seemed really annoyed and gave me a filthy look which made me feel awful!
Yes, she gave you a 'filthy look' because, at that age, his behaviour is your responsibility. She understood that he is a very young child which is why she did not give him a 'filthy look'.