It must be the meat; the only thing I can think is that it's melted fat, but for it to be bitter, it'd have to be rancid, and fat going rancid takes longer than the meat itself going bad, so it's a bit odd. I'd check for larger pockets of fat before cooking (not just marbling) and try steaks from a different source to try and confirm this. Unless... you're not adding fat to the pan or the steak, are you? Something that could've gone rancid, some of which ends up collected in a few places? That'd do it too, of course.
The frequent flipping is actually a really good thing: it makes the steak cook more evenly. Every 5-10 seconds is possibly slightly overkill; 15-20 seconds would probably do too. But in any case, it essentially keeps the heat coming from both sides, so that when the center of the steak reaches the right temperature, both sides are cooked the same amount. If you flip less frequently, you'll tend to end up with one side substantially more cooked than it needs to be. Bonus: flipping frequently also cooks the steak faster! And of course, though in hindsight this all makes perfect sense, I have to give credit to Harold McGee for it. There's a short writeup with great illustrations in this Cooking Issues post.