Whoa - that looks like an exciting journey to take !
There are direct trains but no direct flights for this journey. Bengaluru (Karnataka) to Ajmer (Rajasthan) distance is 2003 km and you can get there by flight + train in just over 7 hours and 50 minutes or by train fares starting from ₹ 633.
The heat there will make you sweat, but it's surely bearable.