General aviation instructor pilot reported a near miss with another aircraft in the traffic pattern of BTA non-towered airport. The instructor mis-judged the closure rate of the other jet aircraft on final; and maneuvered through the final approach course to avoid the jet aircraft.

Narrative

I was conducting a flight lesson with my student and departed from ZZZ; and flew to BTA to conduct touch and goes. Practicing in the pattern we entered the downwind and begun our practice. There was one Aircraft also practicing in the pattern doing low approaches. In the mean time; there was another Aircraft that called a 25 mile final straight in runway 13 at BTA. This was the active runway in use by us as we were doing touch and goes. The second aircraft began getting closer to us with the call out 3 mile final runway 13. I believed we could go past final and head to the west; then proceed to enter midfield and resume our approaches. As we headed to the West I acknowledged on radio I have the Aircraft in sight. However; the Aircraft was coming in at a fairly fast approach speed of around 130 or so knots. I saw them and said on the radio I was descending to avoid them as they were coming in. They pulled up and to the right and then resumed their approach to the runway. Looking back at it I should have either extended downwind or broke off to the east to exit the pattern; giving the Aircraft enough space to land. If I estimated we were about 300 feet from the Aircraft. In the future my corrective actions would be to extend our downwind or break off the pattern in a direction away from final; as the Aircraft is a faster jet than I judged. It was poor decision making on my part.