There are a lot of layers to answering this questions. The best core exercises for bulging discs will vary on the severity and the symptoms you’re experiencing.
Planks for one person may be great but for another they cause pain. So this has to be considered when you are following the suggestion of someone you find online (including myself).
What you’re looking for is to find exercises that both feel good and keep you from doing unnecessary things that could make your pain or bulge worse.
An example of what I wouldn’t suggest someone do is weighted decline russian twists. This is a great way to challenge the core on a lot of different levels but for someone who has a disc sensitivity this would be the LAST thing I have them do.
So the main types of core exercises I try to focus on are neutral spine, anti-extension and anti-rotational exercises.
This is not saying that I NEVER do flexion, extension or twisting with clients but for those I work the most these are rarely seen and are not needed to build more stability around the spine.