Is there airport transfer service? Also, is there an in-house spa and spa price list available online?
yes they have it, spa in house also
I believe the hotel can arrange a transfer on your behalf.
The rooms do not have spas.
I can't really answer your questions as we had been staying right in Ubud prior to our stay in Beji Indah and just caught a taxi out. Fare was 6 dollars Au. Our room didn't have a spa, but perhaps others may have. Your best course would be to contact them with your questions, they are very obliging, pleasant people.
Get an answer from Villa Beji Indah staff and past guests.