From Jaipur taxi to Jaipur airport, fly to Jodhpur airport, then taxi to Jodhpur. 1 h 27 min $104. From Jaipur (JP) train to Jodhpur Junction (JU). 4 h 35 min $15. From Jaipur bus to Jodhpur. 7 h 15 min $10. From Jaipur taxi to Jodhpur. 4 h 49 min $82. From Jaipur drive to Jodhpur. 4 h 49 min $41.
Yes, there is a direct train departing from Jaipur (JP) and arriving at Jodhpur Junction (JU). Services depart 5 times a day, and operate every day. The journey takes approximately 4½ hours.