Can I prevent jail time with a bench warrant?

I was pulled over and issued a failure to stop. I subsequently went into the municipal court to pay fines, $115 with no cash and only my card. I decided to pay it online. After doing so, the screen said successful and I received a text notification saying just that. From then on, I didn't worry about it. Until when visiting my mom’s house, I saw an envelope saying that I had missed a failure to appear. I could face maximum fines and have a bench warrant. I was totally freaking out because I thought I took care of it. I've had money to take care of it the entire time but I didn't know that it wasn't since on the website. It told me there was a payment made on my case. Is there any way to take care of this without jail time? That would jeopardize my job having to spend time in jail. Is it possible to get a netting with the judge to explain?