I myself did B.E(Civil engineering) from BIT, I got placed in Brigade. Later I left as I got admission offer from IIT Kharagpur.
I can say placements for Civil engineering at BIT is far far better than other colleges in Karnataka. Companies like L&T, Shobha, Brigade, Gammon, Simplex and some other local constructions visit campus placements. Around 15-20 will get placed in core engineering, I know it can be no where compared to other branches. But we (Civil engineers) have lot of opportunities outside campus.
Civil engineers have highest number jobs in government sector (Central/State). Civil engineers may start with lower packages of salary, but there is no saturation point. 10 Years back such a huge demand was not there, but now trend has changed. If you seriously interested in Civil..go for it.
One more thing I was CS student in BIT, after my first year I took change branch to Civil. Seriously I never regret that I took wrong decision. I took a right decision, I am happy to be a Civil engineer.