The distance between Maa Vaishnodevi temple and Srinagar is 253kms that is 7 hours journey by road. By air if you are planning to travel, you need to take a road journey of three hours to Jammu airport then fly for 2 hours to Srinagar. There are trains from Katra to Srinagar, but you have to check if they are operational. It’s an overnight journey. By bus from Katra it takes about 10 hours to reach Srinagar. For this from the temple you need to travel to Katra by cab or local bus for an hour to Katra. Then catch another bus to Srinagar.
There is no functional trains between katra to srinagar, the best option is by cab, it will take only 7-8 hours by cab. and if you still want to go by train then you have to travel from katra to banihal by road which is 3 hours journey and from banihal to srinagar you can get a train