Is there any bus service or any transport service rather than a taxi to get to Guilin Airport?

Yes, besides taxi, you can also take shuttle bus at Civil Aviation Hotel or North Railway Station and arrive at the airport directly. Hereunder is the detailed information:
From Civil Aviation Hotel: 06:00 - 21:30 at intervals of 30 minutes
From North Railway Station: 07:30, 12:30, 18:30
The ticket fare is CNY 20 per person.

thank you so much