The blood probably doesn't cause anything, but she could have an infection causing that blood - bacterial vaginosis, yeast, etc (assuming your partner is female) - and you could have that same infection. Bleeding during sex is never a normal thing, and that needs to be checked out.
If your partner is male or trans or non-binary, (or female, for that matter), and you are having anal sex, and is bleeding during sex, make sure you are prepping enough and using enough lube, or he/she/they doesn't have hemorrhoids or an anal fissure.
That all said, NGU can definitely be caused by normal mouth bacteria, or things like adenovirus (usually causes upper respiratory illnesses), strep, and a host of other things. If your partner has been sick, and performed oral sex on you, whatever they had, you can get that genitally.
You don't mention your age, but you could also have inflammation of your prostate. It's more common when you are older, but can happen at any age.
So basically, you need some testing done. Get a urine test done to look for white blood cells in your urine. That will indicate an infection or inflammation. If you have white blood cells, this is NGU. Sometimes, the cause isn't ever determined. You should also get a urine culture done to see if there's any bacteria that indicates a urinary tract infection.
If all that's normal, you should probably then get your prostate checked.
Good luck, and let us know what happens.