My understanding is that you are currently unemployed and on jobseekers allowance. You have been given the opportunity to work for a gym but your main concern is that the cost of using public transport to and from the place of work will be excessive leaving you without enough income to pay all your living costs…
This is a no-brainer. Take the job. Without it you will not continue to receive your jobseeker’s allowance. Once you have a job it is considerably easier to find alternative employment but while you are not employed it will be much more difficult.
In the future you can consider moving closer to the place of employment, but there may also be other options. There may be offers of overtime or an opportunity to apply for a better paid position at the gym. If you are finding it difficult to pay your rent etc. it is also worth looking into whether you can apply for Housing Benefits from your local authority.
Having a job will greatly improve your confidence and sense of self-worth so even if you are in the same financial predicament you are in now, you are much more likely to be able to find an alternative job.
I hope this helps and Good luck!