Pushkar to Ajmer Bus Depot distance is 15 km approx.
To reach Ajmer Railway Station from Pushkar, Government buses are available from the 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 the 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).