would I ever be able to go on birth control and NOT spread HPV to my partner?

This is a great question and one that women are so often unclear on. As Susan said condoms provide some protection, they are about 70% effective against spreading the virus.

I want to give you some information about birth control and HPV that you should consider when deciding to start taking oral contraception.

There is emerging evidence in the literature regarding the correlation between hormonal contraception and cervical dysplasia.

The risk for developing cervical cancer with less than 5 years of hormonal contraceptive use is 10%
With 5-9 years of use the risk increases to 60%
With 10 years of use the risk increases to 120%

The risk declines after discontinuing hormonal contraception and by 10 or more years the risk returns to that of someone who has never used hormonal contraception.
Bottom line is that with increased use of hormonal contraception there is statistically significant risk of developing cervical cancer.

One of the ways in which hormonal contraception impacts HPV and cervical cancer is by increasing estrogen receptor expression in the tissues. HPV 18, one of the strains correlated with cervical dysplasia and cancer, has been shown to directly interact with estrogen receptors whether estrogen was present or not. Also, an in-vitro study showed that estrogen stimulates the growth of HPV positive cervical cancer cells.

The risk factors for developing HPV related cervical dysplasia are:
Smoking
Oral contraceptive use
Early onset of sexual intercourse (before age 16)
Multiple sexual partners
Unprotected sex and condom use (condoms are only 70% effective against HPV exposure)
Uncircumcised males
Multiple pregnancies
HIV
Chlamydia infection
Herpes infection
Obesity
Low socioeconomic status
Diet
Screening Pap smears (lack of)