Pushkar to Ajmer Bus Depot distance is 15 km approx.
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.
( Above said is as per travel I did recently during Pushkar tour )
Update
Now-a-days Pushkar is having its own railway station.
One can catch a train from Pushkar Railway Station (15:40 pm) to reach Ajmer Railway Station (17:00 pm).
Distance from Pushkar to Cities
Bikaner is 253 km and Merta City 59 km approx. from Pushkar via National Highway 89.