Yes one partner can have trichomoniasis and not the other.
Your partner may have trichomoniasis for months and not know about it and then they may unknowingly transmit the trichomoniasis onto you.
You can also get trichomoniasis without cheating on your partner.
Your partner themselves may have the trichomoniasis without you or them knowing about it and then it gets transmitted to you when you have sex.
It's also entirely possible for a woman to get the trichomoniasis infection on her own even without a partner.
Yes it is possible for a woman get trichomoniasis on her own.
You can get trichomoniasis on your own by touching your genitals without washing your hands.
The trichomoniasis can be transmitted through touching surfaces such as a public toilet flush handle, bathroom door, faucet etc.
Most commonly the trichomoniasis is transmitted sexually and you may get it and have the trichomoniasis through a previous relationship.
Some woman can have trichomoniasis for months and not even know about it.
So while the trichomoniasis is usually contracted and transmitted sexually it is possible to get the trichomoniasis even without having sex or being sexually active.