How can I visit poeny garden and Longmen Grottoes in one day from Xian?

You can do it in one day. It is suggested you take a bullet train from Xian North Railway Station to Longmen Train Station in around 1.5h. Upon arrival, take bus no. 75 for nearly 1h to Xiyuan Lu Qingdao Lukou stop. You will see the poeny garden the moment you alight from the bus.
After visiting in the garden, get out from the eastern gate and walk northwards to reach Jinghua Road, go westwards along Jinghua Road to find the bus stop of bus no. 60. Take that bus to go directly to the grottoes.
When you finish your visit at the grottoes, either take a taxi or bus no. 67 to reach the Longmen Train Station for your return train to Xian.