I was taking enbrel, and then was treated for latent tb as well. I had to stop taking enbrel for the duration of treatment, but remained on the methotrexate. Both Rheumy and infectious disease doctor felt that methotrexate was fine to take--enbrel was the problem. Nevertheless, I can see why a doctor would be super cautious and require patients to stop all meds.
It's been a while, but I believe the tb treatment lasted for at least 2 months, maybe more. My joints got all swollen and sore again. But finally, the treatment was over, I restarted enbrel and have done well ever since.
It was not a great time in my RA treatment, but I'm glad it's over with. I don't have to be treated for latent tb again.
Hope you handle the treatment well, and are back on your meds sooner than you think.