I think that someone with more knowledge of the Canadian system should provide a political answer—or edit this answer, to put this information in context—but here is a technical one.
The Canadian parliament posts all of its business on line in English and in French. Those links provide a lot of data on issues like committee meetings and scheduled hearings.
More directly related to the bills, there is a list of bills before parliament including a "progress tracker" on each bill. That page has XML and RSS feeds which will allow you to follow a variety of issues indirectly. As someone who doesn't use social media, but who apparently is interested in politics, you can either use the RSS or XML feeds directly to follow the bills before parliament or you can pair those feeds with IFTTT to create a digest e-mail, text alerts and so on as you like.
One word of warning: the more "raw" the data are, the more analysis they require to become information. It may be appealing to read "raw" data, without any interpolation, but at the same time, absent context it can be unhelpful and sometimes even deleterious to your understanding of the system. For example, bills are often proposed that will never, ever make it, and sometimes parliamentary procedure and other arcana will slip past a casual observers eye.
For this reason, it is important to fully understand the processes, and that is what analysts do. While all analysis is at least tinged with some bias, the best analysts are accurate in spite of their biases. On many issues, the bias won't matter either (e.g. That bill is dead in committee.) If you are truly interested in learning more about Canadian politics, this is an excellent start, but take the time to educate yourself about the larger political world well, and seek out reliable analysts.