A 'squirt' could refer to going to the toilet in this context, though it is neither polite nor common. I can imagine a little boy saying it to his friends.
If you wanted a polite way to say you need to go to the bathroom, you could say:
'I am going to the restroom/bathroom.'
'I have to use the toilet.' Is also acceptable.
'May I use your restroom/bathroom?' If you are asking permission.
An old fashioned way of saying that you have to go to the toilet used by women is, 'I am going to powder my nose'. Please note men do not say this.
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