I know this must feel embarrasing, but believe me, your doctor has heard many, many stranger things.
First, yes different strains of the virus that cuases warts cause the different types of warts on your body. Genital warts can be a different strain from a wart on the foot, for example. And yes, you're right to think that it would take longer than 1/2 day for your girlfriend to transfer a wart from her knee to your anal area, so you can relax about trying to explain that to your doctor. S/he probably doesn't need to know that part at all.
But you do need to have this evaluated. At age 20, it's extremely, extremely unlikely that you have any sort of cancer, for example, or anything bad at all, but what you want to learn from a doctor's exam is exactly what this bump is. It could be any number of things. For example, it could be a small hemorrhoid. It could be a mole that has grown or changed shape. It could be any of a number of other benign skin conditions. It could be an ingrown hair that led to a slight infected hair follicle. It could be a different type of sexually transmitted disease, such as herpes.
Of course, it could be a wart after all, one that was transmitted by your girlfriend at an earlier time. So that's why you need to have an exam and tell your doctor what you noticed, when you noticed it, and that you are sexually active. That should be sufficient information for the doctor to begin to evaluate this bump.
Girls can have internal genital warts, in their vagina, on their cervix, without ever knowing it. So your girlfriend should see her doctor to have a simple, painless exam to check this out. If she has internal warts, she can have them treated easily. This would be very important because, if gential warts are left untreated in a girl for too long, they can develop into a pre-cancerous condition, which could then lead to cancer of the cervix. But, if internal warts are caught early, this is completely treatable and any cancer is preventable.
So, in the end, it could be a wart transmitted from a previous time, but you really need to go to your doctor to find out for sure what it is, and to have it appropriately treated. And your girlfriend needs to have GYN exam done also. Don't be nervous about the doctor. Just tell him/her that you have a "bump," or "maybe a wart" near your anus and need to have it looked at. When you see the doctor, let him/her know that you are sexually active. S/he will ask you more questions about your symptoms, and will need to look at the area, but they are professionals whose job it is to make you feel comofortable. Trust me, they see lots of people with similar complaints/concerns. In fact, this one wouldn't even register on the "unusual" radar, because it's so common.
I hope this information helps you. Please let me know if you think I can add anything else, or if you think of additional questions.
Mary Jean, RN