I would like to calculate the Conductivity (µS cm-1) from summation of the concentration of Chloride and Bicarbonate (mg/l), is there any equation of factor to calculate conductivity?
You cannot convert the unit of liquid concentration of mg /l to the conductivity of µS cm-1. They are different measurements for different physical values.
You should check for molar conductivity textbooks. Each ion has a conductivity, depending on its charge, size and mobility. Normally small ions such as H+ and OH- contributes a lot to the conductivity of your solution. There are tables everywhere with the molar conductivity of common ions, so with the values of each ion and their concentration you can estimate the total conductivity of your system.
Check this document: https://hal.sorbonne-universite.fr/hal-01974195/file/conweak2_revised.pdf
You can also check this paper: Article The Effect of the Humid Air Plasma on the Conductivity of Di...
The calculations are quite simple. Search for Kohlrausch's Law