In this work, we have performed systematic shell-model calculations for Bi isotopes with $A=$ 204-213 using KHH7B and KHM3Y effective interactions. We have reported yrast and non-yrast shell-model states corresponding to the available experimental data. From the comparison with the experimental data, we could assign spin and parity of several unconfirmed states. We have also calculated electromagnetic properties and compared them with the available experimental data and predicted where experimental data are not available. This study also includes a detailed discussion of multiple isomeric states based on computed shell-model configurations and their respective half-lives.