BBA

It depends upon which institutes that you pursue your course. Normally for BBA graduates, salaries would be 3-4 lakhs per annum which is the average salary that are received. But it is completely based on institution. So choose the best institution, check the placements, companies, average salary accordingly you have to take decision to join.
A graduate from top b schools like IIMs receive a salary of 7-12 LPA. You can do MBA after BBA to get a good salary.

I am wondering if Patna University is good for anything except getting a government job and getting a government approved degree. I haven't studied there and have no intention either, definitely there isn't a single good institute in Bihar for business management and professional courses be it engineering medicine or anything. For a government recognized degree, you may opt.

There are a number of job opportunities after BBA in aviation like:
Customer Service Management
Customer Relationship Management
Passenger Reservations & Ticketing
Revenue Management
Airline Sales & Marketing
Flight/Data Analysis
Loyalty Programs Management
Fueling Management.
The salary packages can be in the range of 3-5 Lacs per annum if you do it from a reputed college like UPES, Dehradun,

Talking about scope and career prospects, it is safe to say that in the near future. Aviation sector is all set to grow even more. Along with the growth, the sector will need more and more management professionals to handle airport management tasks. So, BBA airport management professionals wont run out of job opportunities! One may also follow up BBA with an MBA degree and thus increase ones qualifications. Starting salary is around 20-25k INR per month.

If you want to be a part of airport management/operations, then you need to pursue a course in aviation & hospitality management coupled with some business management skills. You can go for MBA in aviation management.

I think you should do BBA and also, opt for Masters with specialisation in marketing.