Travelling to India with passport that expires soon

I am traveling to India in a week, My passport expires in 4 months, Will I be able to enter Bahrain with only 3 months' passport validity? Does the 6-month minimum validity requirement apply to residents?  My resident permit is valid till August 2023.

Yes you can enter if your visa is valid. 

My wife's passport is due for renewal in June 2023 and she arrived last month from India. She has a valid residence permit

The passport validity applies to visitors only; not Bahrain residents or Citizens.