Some relative and absolute $\ensuremath{\gamma}$-ray transition probabilities have been measured for the low-lying levels in $^{209}\mathrm{Bi}$ by observing the Coulomb excitation and subsequent decay of the states. Thick bismuth targets were bombarded with 19-MeV $\ensuremath{\alpha}$ particles, and $\ensuremath{\gamma}$-ray yields at 0\ifmmode^\circ\else\textdegree\fi{}, 30\ifmmode^\circ\else\textdegree\fi{}, 45\ifmmode^\circ\else\textdegree\fi{}, 60\ifmmode^\circ\else\textdegree\fi{}, and 90\ifmmode^\circ\else\textdegree\fi{} were observed with a 25-${\mathrm{cm}}^{3}$ LiGe detector. Determinations have been made of the transition strengths to the ${f}_{\frac{7}{2}}$ (0.897-MeV), the ${i}_{\frac{13}{2}}$ (1.608-MeV), and the ${f}_{\frac{5}{2}}$ (2.822-MeV), and the septuplet of levels near 2.6 MeV, formed by coupling an ${h}_{\frac{9}{2}}$ particle to the ${3}^{\ensuremath{-}}$ octupole state in $^{208}\mathrm{Pb}$, excited by $E2$, $E3$, $E2$, and $E3$ Coulomb excitation, respectively, Approximate $E1$ transition strengths for ground-state decays of the 2.563-, 2.581-, and 2.598-MeV levels have been determined from the Doppler broadening of the $\ensuremath{\gamma}$ peaks. Branches are observed corresponding to decays from the 2.741- and 2.600-MeV states to the 1.608 (${\frac{13}{2}}^{+}$) level, and from the 2.822-, 2.615-, and 2.581-MeV levels to the 0.897 (${\frac{7}{2}}^{\ensuremath{-}}$) state. The $\ensuremath{\gamma}$-ray strengths and relative transition rates are compared with the predictions of a particle-vibration coupling model.