Thank you all so much for your thoughts! Thankfully, the bright red bleeding seemed to just be random, and all is well. The nurse couldn't find any other areas that should cause any concern or more bleeding.
And, we got to see the heartbeat! I was worried it might be too early to see, and I would be left in limbo, so it was another big relief. I am on pelvic rest as a precaution until my next appointment, which is January 17th. The nurse told me to go ahead and be a couch potato for a while, too. I think I can handle that.