The capture cross section of $^{209}$Bi(n,$gamma$)$^{210g}$Bi was measured at different astrophysically energies including thermal capture cross section (25 meV), resonance integral, and the Maxwellian averaged cross section at a thermal energy of $kT$ = 30 keV. The partial capture cross section ($sigma_g$) was determined using the activation technique and by measuring the $^{210}$Po activity. The newly developed and tested NICE detector setup was used to measure the $alpha$-activity of the $^{210}$Po. Using this setup the thermal and resonance integral cross sections were determined to be $16.2;pm;0.97$~mb and $89.81;pm;8.0$~mb, respectively. And the Maxwellian average cross section was measured to be $2.01;pm;0.38$~mb.