This gives both you and the tenant an easy to budget mark.I would write up an addendum to agree to this arrangement.

Unless you suspect there is a willful neglect, bad hygiene or mental health aspect that caused the bed bugs and wasn't just bad luck, don't evict; have them do a written payment arrangement.

Any suggestions on how I would structure such an arrangement?

Clean, flower pots, etc. 

They collect rents, arrange repairs (though run things by me that are "major" or in-excess of $250).  

That means finding as many other agents in the area as possible who can confirm or deny that arrangement.

I had arranged everything with the title Company doing the closing however they did not follow the process (that they acknowledge in writing) to get the funds from the 1031 intermediary.

I've even arranged for both myself and the seller (who should have a relationship with the current tenant) to go meet with the current tenant to inform them the property is being sold and letting the tenant know what your intentions are (to be a very good landlord) and to ask them what their intentions are..Again, best of luck with your REI!!

The amount I receive in rent covers most of my mortgage payments, allowing me to save most of my income which I plan to use for more properties in the (near) future.I haven't set any systems in place to make our arrangement seem formal.

No, you both would not have to live there with this arrangement.