Whenever you find the need for a thread-safe List<T>, in most cases neither the ConcurrentBag<T> nor the BlockingCollection<T> are going to be your best option. Both collections are specialized for facilitating producer-consumer scenarios, so unless you have more than one threads that are concurrently adding and removing items from the collection, you should look for other options (with the best candidate being the ConcurrentQueue<T> in most cases).
Regarding especially the ConcurrentBag<T>, it's an extremely specialized class targeting mixed producer-consumer scenarios. This means that each worker-thread is expected to be both a producer and a consumer (that adds and removes items from the same collection). It could be a good candidate for the internal storage of an ObjectPool class, but beyond that it is hard to imagine any advantageous usage scenario for this class.
People usually think that the ConcurrentBag<T> is the thread-safe equivalent of a List<T>, but it's not. The similarity of the two APIs is misleading. Calling Add to a List<T> results to adding an item at the end of the list. Calling Add to a ConcurrentBag<T> results instead to the item being added at a random slot inside the bag. The ConcurrentBag<T> is essentially unordered. It is not optimized for being enumerated, and does a lousy job when it is commanded to do so. It maintains internally a bunch of thread-local queues, so the order of its contents is dominated by which thread did what, not by when did something happened.
These characteristics make the ConcurrentBag<T> a less than ideal choice for storing the results of a Parallel.For/Parallel.ForEach loop.
A better thread-safe substitute of the List<T>.Add is the ConcurrentQueue<T>.Enqueue method. "Enqueue" is a less familiar word than "Add", but it actually does what you expect it to do.
There is nothing that a ConcurrentBag<T> can do that a ConcurrentQueue<T> can't. For example neither collection offers a way to remove a specific item from the collection. If you want a concurrent collection with a TryRemove method that has a key parameter, you could look at the ConcurrentDictionary<K,V> class.