If you're on a teacher training course then perhaps you have to, like nursing and medical students, tell the university immediately when you're charged with a criminal offence.
If you're already in a situation where enhanced DBS is required, it would make sense for disclosure of new convictions to be required and perhaps charges.
In any case, if you are on a course which stipulates disclosure you should have been notified of and agreed to this before the start of the course; we might also expect this information to be on the university website.
You haven't said whether you have consulted the student union as
@WesternLancer and
@Western Sunset have suggested: that would seem a good idea for potential advice on legal, career and perhaps welfare aspects.
I can't vouch for how accurate or up-to-date these are, but this may be useful:
Aim of this page For entry to all professional and Postgraduate Certificate in Education (PGCE) courses in England and Wales […]
unlock.org.uk
and "Working as a teacher" here:
Explore our criminal record advice and guidance about disclosure in different job types. Find out what you need to disclose. See more.
www.nacro.org.uk
Unlock and Nacro have helplines - they may prefer it if you consult their websites before calling.
Hopefully you can find the offical information on regulation of teachers, disclosure, procedures and so on as well as guidance on how employers view convictions and the behaviour which they may learn about in interviews following disclosure - and how to demonstrate trustworthiness.
Where the main issue is fitness to work in a type of job, it's important to bear in mind that it's about the future, so what someone does after they're caught breaking the law could make a big difference.
Please bear in mind that the charge here is for much less than you actually did, not just in terms of the number of offences but also because the offence you're charged with implies no dishonesty.
People sometimes think that as a result, the consequences would be milder than for an offence which does include intent to avoid a fare. That might happen if there is a "tick-box" exercise, and no questions about what happened to bring about the conviction. But for professions like teaching, the system involves humans making decisions about fitness to work, and sensibly, the idea is to find out what the person actually did, what they did after being caught, and/or how they are now approaching the situation.
Someone might say this is a minor matter and doesn't show a risk to children. What I have partly in mind is that because of the difference between what you did and what you're charged for, you may at some points need to make choices about what to disclose and when. If a person is seen as being less than candid at the time of interview, that can be a bigger matter than the original crime.
In some circumstances, for example, a person might only reveal the byelaw offence without disclosing the other offences or the dishonesty - perhaps wrongly thinking that is all that is required. And in some circumstances that might be viewed as less than frank. So you need to be informed, think in advance, make sure you are clear what is being requested, and be prepared to be open.