Is it advisable in my case to take a second bachelor's degree?
In almost every circumstance, one bachelor degree is enough. Even if it's from a less-than-ideal program, as long as you can show that you performed well, it will at least count for that.

If you are really that concerned about how your school appears on your academic record, I suggest trying to enroll in a Masters program at a more reputable school. Performing well at this level will allow you to improve your understanding in your field (and potentially fill gaps that were overlooked in your evidently underwhelming bachelors program) and demonstrate your abilities.

If for some reason you are unable to obtain admission to a Masters program, there are always non-credit or non-degree-track courses out there that you can take to bolster your breadth and depth of understanding as well as your credentials. Then, if you're still not satisfied, you can always reapply to those graduate programs.

But moral of the story, a second bachelors is not worth the time and money. Even once you have it, it doesn't say half as much about you as a graduate degree would in the same area. Top performance at the graduate level will allay any concerns about your undergraduate academic experience.