I agree with Joe. Chances are there are other members of your parish who would love to sit and discuss and learn more about the faith. Starting a Bible study group isn’t hard at all. Just talk with your priest about it. Even if his schedule doesn’t allow for him to be present at every meeting, he may be able to recommend some books or other resources, and perhaps one of the deacons may join in. It can even be advertised in the weekly announcements, and your priest could even make an announcement at the end of Mass so that the congregation knows the meeting times, place, etc.
You’d be surprised how many people would show up.
As far as the non-denominational study group, personally I would not take that particular path to learn more about the Catholic faith. I’ve attended plenty of study groups in my time, and generally enjoyed the good conversation and met some very nice people in the process, but unfortunately (in my experience) most non-catholics have practically zero knowledge of the history of the Church, know little or nothing about the saints, and can often times have a very skewed understanding of Catholic practices. (One I hear a lot of is that Catholics are idolaters, or that we worship Mary and the saints, which of course is false.)
Also, as someone else mentioned above, you never really know if what you are hearing at a non-denominational meeting is fact or opinion, which is unfortunate. I notice a lot of the time scripture is taken our of context, or purposefully skewed to fit an individual’s own agenda.
I once sat through a Baptist sermon where the pastor declared alcohol to be the true root of all evil, and then went on to explain that Jesus did not turn water into wine at the wedding feast, but rather created a non-alcoholic grape juice… which makes no sense. If he would have read a few lines further he would have had to read the bit about ‘saving the best for last’ and a paragraph further would have been the inebriated fellow falling out of the window.
I mention this merely as an example. Also, Protestants in general usually don’t have a very good grasp of what the Sacraments are, or how they are to be used, and when.
non-denominational prayer groups can be a lot of fun, and a great way to meet people or even try to spread a better understanding of your own faith, but in my experience they simply aren’t the best way to actually learn about the Catholic faith.