Yes, it needs 2-2.5 hour from Zhengzhou to Luoyang. As to lowest airlines, you can search for the price info at:
www.travelchinaguide.com/china-flights/Flightsearch.asp
Other option, you can take bullet train from Beijing to Zhengzhou, 5 hours, if the air ticket that day is not cheap. Just to stay at the city when you first arrive in from Beijing. If you stay in Zhengzhou, you can get to Luoyang first and then take Bus 81 at Luoyang Railway Station to the grottoes. If you stay in Luoyang, you can take bus to Dengfeng first and then change to public bus or taxi to Shaolin Temple.

Dear Jonh,

Many thanks for your very clear information.
However, i finally selected trip to Hangzhou and Suzhou instead. If you are the person from Travel China company then please help to offer me car rental for below program:
We are 3 persons would like to travel as following itinerary. Please help to quote

4Nov: PEK-SHA
Pick up at airport and transfer to hotel in Shanghai. Hotel name TBA
PEKSHA: MU5156 (1745-2000)

5Nov: SHA – Suzhou
07h00: pickup at hotel and take quick SHA city tour for for viewing the harbor, TV tower (just seat in car) then heading to Suzhou. Tour in Suzhou.
18h00: Transfer from Suzhou to hotel in Hangzhou.
Hotel TBA

6Nov: HGH – PEK
Fullday tour in HGH and transfer to airport for PEK
HGHPEK: MU5161 (1905-2105)
Pick up and transfer to hotel. Hotel name TBA

7Nov: PEK
Fullday tour in PEK including great wall, Ming 13 Tombs, Heaven Temple
Hotel TBA

8Nov: PEK - HAN
Half day tour in PEK including tour to forbidden palace and Summer Palace.
Transfer to airport for departure.
VN0901: 1530-1820

Thanks
Hanh