How to determine value of Vbe ON in BJT
Unless your data is very precise, and includes values very close to VCE=0, you won't have enough information to determine VBE precisely.

Generally the VBE will be around 0.65 V for most transistors while operated at 'normal' collector currents. If you operated at 1/100 of this value, VBE would only change by about 0.12 V. If you operated at 50 C hotter than room temperature, the VBE would also only change by less than 100 mV. So if you don't need a value more precise than that, I'd suggest using 0.65 V as a good estimate.