It seems like there are factors involved with this that might not be inherently obvious. Nobody can deny that you've invested time and money to take your girlfriend to an event that you likely didn't need to attend at all. If she had the capability to take her own car or ride with someone else, she would have likely feel more financially obligated to the trip. The same if you had taken a friend, coworker, or classmate; you'd expect to have them cover most of the personal expenses for helping take them to their event. Although, in that situation, the discussion should happen prior to the trip.
The thing with relationships is that every action is a form of investment. Whether you're taking the time to talk with her; carving out some of your day to do an activity; or you're paying for a trip, it's all benefiting the end goal of building your relationship closer. If this were to end with you sticking it out long term, marriage makes it so neither of you really have your "own" money anymore, so it'd be moot to ever ask in that situation. This doesn't mean that you should overly burden yourself or feel like you're giving so much more than she does. It seems justified that you feel like the financial loss of the trip is worthwhile to approach her and try to recouperate at least half of the cost.
Approach is Key
The way that you structure your sentences and the words you use will play a drastic role in how willing the other person is going to with you. You use the word "charged," which is a pretty strong word that makes it seem more like a demand or forced debt that she has, even though she had no reason (from her perspective) to see it coming. Another factor is her life experiences growing up. If she's under the impression that gender/relationship roles (e.g. men are responsible for A, B, C; women are responsible for X, Y, Z) are a thing that she expects, then your ability to fix this situation will hinge on if you can bridge that. To her, she may expect that you will cover more of the expenses in the relationship, which may also have appeared if you've went out to the movies or dinner together.
To me, it feels like there are two ways you could have approached her to try and receive some money for gas: logically or emotionally.
The most obvious retort I'd have given was that you would agree that both of you took the trip together and that it was a great experience... however, only one of you paid for the trip. You could argue that you're willingness to still pay for half is your acceptance that you both gained something from the trip (bonding experience, mainly). Other answers provided good points that you could pose that she pays for the next 4 hours of traveling costs.
Using lighter words that draw sympathy or have her feel in control of the decision may result in a more promising response. Somewhere along the lines of
"I was looking back at how much we spent on the trip yesterday and I was surprised to see that we went through $60 in gas. That's quite a bit of money to just get to and from the event. Is there any way you'd be able to contribute towards that cost in some way? Part of my wallet hopes that we could meet somewhere along the middle. Really anything would help, but I just want to make sure we both feel at ease over the expenses we paid."
It's more indirect and has "we" scattered throughout, which is very important to ensure that subtle reminder that you were both involved in the trip. This does leave the option open that she says she doesn't feel the need to pay, but you're asking for a sort of mercy that you don't get stuck with the full expenses.
I've incorporated both the logical and emotional scenarios in my day-to-day life. My career is in computers, so I tend to lean more towards using logic since that's more what I'm familiar with. However, I think the situation guides what is best, not preferrence. If I'm arguing over something that has a bunch of opinions or little to no facts to back them up, I'll go the logic route. If I'm awkwardly having to talk with someone or ask for something, I'll go the indirect/sympathetic approach. It feels a bit more like you're social engineering, but there's nothing wrong with gaining skills in that as long as you're moral in your goals.