Congratulations for graduating, and with two jobs in hand
It is really confusing when you have several desires and are not sure which would be better to go for first. Clearing CAT and studying from a premium institute gives us an edge to get into managerial positions along with an increase in pay. Another reason for pursuing MBA is to change domains! What I personally think it is always preferable to have some experience before anyone goes for a PG (specially MBA). It gives you a better clarity regarding your aspirations and the world demands. In fact, you also get extra credits for your experience during your MBA interviews, which makes it easier to get through
Clearing Civil services helps us to get into government's administration and work closely with them for the grassroots. Civil services has age barrier of 32yrs for general category students along with 6 maximum attempts. As you have just graduated, and have offers in hand, I think you can go ahead to start your preparation a little later as well. Civil services, being one of the toughest exams, requires a lot of hard work to get through, and the exam process too is time taking.
Give it a thought about why you are not interested to take up a job as a job has several avenues attached to it. And today most companies look for a candidate's readiness to learn. You are just getting into the job market so there is going to be a lot to learn at the job as well as off the job - culture, industry, interactions, etiquette, ethics, various teams in companies along with your job role! Dear, there will always be times when we don't like few things but it is okay at times to accept those for a better future. The way you handle yourself in such times also matters because they are sure to appear - be it your pvt job or as an IAS or even life in general.
What is important is that you can carry on the learning at the job into your MBA! And as already shared, you could also choose to pursue MBA through correspondence anytime later. Executive or part time options will also get available for you as you get some experience. Many govt employees in the top cadres are even sent to the premium MBA institutes later on as well as they are able to handle their duties with better productivity when they finish the course. So give everything a thought for a day or two. And then take your decision! Hope that helps! You are always welcome to chat with anyone here for any further directions! Take care!