They prefer бізнес-леді as far as I know
For a lot of professions it's okay to use masculine forms for women, but not for those that have "man" in it.
This is a bit of a general question, as this has happened to me several times, but because it came up here - is the course inconsistent about how it accepts і and и? Because I regularly mix these up (I spelled buisnessman here as бизнесмен with an и) and I'm wondering why it still accepts my answer as correct. It doesn't even tell me that I've made a typo!
That's not the course's fault, that's just (unfortunately) how Duolingo works.
When you type your answer in Cyrillic, Duolingo first transliterates it to Latin and than back to Cyrillic to check your answer. Because of that double transliteration and because there are different Cyrillic alphabets in different countries (Latin i corresponds to Ukr i and Russian и), such problem exists
How frustrating! Well, I shall just have to make sure to double-check the answers to ensure that I have the correct spelling then :)