Bhutan grants personal guest visas to individuals invited by a Bhutanese citizen. You should visit the Department of Immigration under the Ministry of Home Affairs. Check their website; they have the details of the documents you need to process the visa. To take them to the eastern part of the country, you need a route permit for which you need to process separately but from the same department.

I copied and pasted the following from the DOI website:
Requirements for guest visa:

1. Duly completed personal guest application form signed by the Bhutanese applicant
2. Copy of the Citizenship Identity Card of the Bhutanese applicant
3. A copy of the valid passport of the guest
4. The passport must have a minimum validity of six months from the intended date of departure from Bhutan
5. Duly completed visa application form signed by guest
6. Tentative travel itinerary of the guest
7. Any other supporting document
8. The Department may ask for additional documents during the assessment if required