Pushkar to Ajmer Bus Depot distance is 15 km approx.
To reach Ajmer Railway Station from Pushkar, Government buses are available from Pushkar government bus depot for Ajmer Bus Depot – Rs. 10 the fare. Ajmer Bus Depot to Ajmer Railway Station sharing autos are available outside the Ajmer bus depot for Rs. 5 per person.
(The above said is as per travel I did recently during the Pushkar tour)
Update
Nowadays Pushkar has its own railway station.
One can catch a train from Pushkar Railway Station (15:40 pm) to reach Ajmer Railway Station (17:00 pm).