Bachelors

hii , My answer is NO, it's not worth at all to pursue for bachelor's of jewellery designing from distance learning. Because jewellery designing is more of like a practical subject, you wouldn't learn anything properly in a distance programme. And it's not only about INDIA, it's the same thing for any other country. If you can't give time to it then I will suggest you to go for a full time short term diploma ( like one year diploma ) instead of a distance Bachelor's degree. You need to practice it regularly.
I hope now it's understood for you. Also if you want to pursue for a bachelor's only then accessory designing is a better idea than jewellery designing. Because in accessory designing apart from jewellery you will also learn about other products & goods and explore much more materials than jewellery designing .

I am afraid that there are any specific government college for mass communication, there are many colleges that provides Bachelor's degree in Journalism precisely, but not Mass communication. Journalism is just a mere part of Mass Communication that has various fields inside, so if you want to pursue your career in just Journalism then DCAC, IP University are some of the leaders in the stream considering they are under government. Rest the fees structure in private colleges are also not that high and in fact you get the same exposure in both the sectors. See, both the colleges will follow the same course structure with the same facilities, gone are those days when being a graduate from government colleges will fetch you a better job. Now, Companies hunt for raw talent and people who know how to do the work assigned to them. So, you keep yourself available for private institutes also.