I'm going to refuse to carry a strangers child on my lap for an hour's bus ride
Why would they ask you to hold their child?
It's not even my child they should do it.
You can say no to anyone you want if you don't want to do something. They should be expected to take care of their own child not strangers.
I think being forced to carry around a pregnant stranger's kid for an hour is wrong.
There is nothing wrong with saying no to strangers when they ask you to do something. You are not obligated to help them especially when there are children involved. If it makes you uncomfortable just be straight forward with them.