When you just wanna go to bed,’nemutai’ can be used. It means literary “I am sleepy”, but it is taken you wanna go to bed, in houses.
If someone is talking to you endlessly but you feel sleepy, then you can say, ‘nekasete kure’ (let me sleep).
‘nemutai / nemui ?’ = are you sleepy? , do you want to go to bed?
We don’t have “Hey babe”. You would say some adequate pronoun or interjection for the scene.