HIV negative woman and her positive partner can conceive naturally, however you run the risk of acquiring HIV from unprotected intercourse.
The only 100 % reliably safe way is to have sperm washing of your partner's semen sample and then undergoing IUI ( intra uterine insemination ). As you have mentioned, this would be expensive.
If you decide to conceive naturally, it should be an informed decision, going ahead while understanding the risks involved - both to you, and your baby, whom you would infect in turn, if you get infected.
To make this safer, your partner must have an undetectable viral load for at least 6 months. Your chances of becoming HIV positive from having unprotected sex will depend on many factors. These include;
The viral load in your partner’s semen
The type of sex you have
The presence of sexually transmitted infections for either of you
Limited conception attempts made during ovulation may carry a low risk if your partner’s viral load is undetectable.
However, there is still a risk involved even from a single act of unprotected exposure.
The risk of transmission is very low when your partner has an undetectable viral load for 6 months. However, the risk of transmission is still not zero.
HOWEVER I RECOMMEND going for artificial insemination even if it is costly. Even though this is costly this is the best measure considering the risk involved otherwise.
All the best.
Please feel free to ask for further clarifications.