If you haven't had any symptoms for 3 years, your body has cleared the virus and you aren't infectious any longer. HPV is not a lifelong infection.
HPV is only infectious from the site of infection. If you have genital HPV, you aren't infectious from your mouth, so kissing is fine (and kissing isn't a risk for HPV). If you still had HPV, unprotected sex would definitely transmit it, but you're fine now.
Keep in mind that there are well over 100 strains of HPV, and over 30 of those affect the genitals. You can have more than 1 strain at a time, and you can have strains that show no symptoms. It's estimated that about 90% of us will get HPV at least once in our lifetimes. Many experts call it an inevitability of sex now.
If you and your girlfriend have had other partners, you should both test for other STDs before engaging in unprotected sex, and be sure to talk about birth control. There are also vaccines available for HPV, so you both should talk to your doctors to see if you're candidates for it.