Pack some nice homemade food, cause this isn't a short trip !
There are direct trains but no direct flights for this journey. Mumbai (Maharashtra) to Ajmer (Rajasthan) distance is 1041 km and you can get there by flight + train in just over 6 hours and 55 minutes or by train fares starting from ₹ 389.
The heat there will make you sweat, but it's surely bearable.