What to do about a hyperverbal classmate?

I have a classmate with whom I've spent the last 5 weeks on a clinical rotation. I'll be spending the next 5 weeks with this person as well, and we may, in fact, end up on the same rotations for the remainder of the year, which is 2 more quarters. This person is friendly and outgoing, but after being in their presence for some time, it's become clear that they're quite self-important, self-serving, and passive aggressive. This wouldn't normally be of much concern to me (not my business what kind of personality you have, as long as your life isn't intertwined with mine in some inextricable way), except that they talk incessantly. Truly, our 1-hour post-conference meetings are dominated by endless, rambling chatter, and 8 of us, including the clinical instructor, can be held prisoner for upwards of 15 minutes as this person answers 1 question. Often, this occurs several times during the course of one post-conference. Sometimes other classmates will begin talking only to be interrupted mid-sentence by this hyperverbal person interjecting their opinion. The quieter students get shut out completely, and never have a chance to say anything. The impression I get is that most people start to tune out after several minutes. My problem is that I can't seem to do this, and so it grates on my nerves that are already usually frazzled by the end of the day.

As an example of the type of rude interruption and inappropriate amount of talking:

Yesterday, a classmate and I were going over some IVBP procedures, and this classmate interrupted me as I was running through my practice no less than 3 times in about 5 minutes. Once was because they wanted to share a text that their significant other had just sent them.

I've never enjoyed these types of personalities who were very much "me, me, me, let's talk about me...forever," but I've mostly been able to avoid them. At this point, it's clear that avoidance isn't going to be possible with only 7 other students on this rotation. Short of that, is there a way to politely tell someone they're talking too much? Interrupting back is just going to perpetuate rudeness and isn't going to get me anywhere, and I don't think this person is aware enough that they would take the hint anyway. Being unfriendly is simply impossible with our small class size. Do I need to just suck it up, and play nice, or is there a way to tactfully tell someone to shut up?