Pack some nice homemade food, cause this isn't a short trip !
There are direct trains but no direct flights for this journey. Travelling by train is the cheapest way of getting there. Bengaluru (Karnataka) to Ajmer (Rajasthan) distance is 2003 km and you can get there by train in just over 43 hours and 35 minutes. However, flight + train tickets come also cheap with fares starting from ₹ 4758.
The weather is amazing right now. You'll have a great time.