Even you would like to marry her as pr Muslim personal act, the marriage can be registered only under foreign marriage act or special marriage act since she is a foreign citizen.
For getting legal validity for the marriage the marriage has to be registered under special marriage act by following the procedures meant for it accordingly.
In India, civil weddings are governed by the provisions of The Special Marriage Act (1954). Under the Act, there’s a 30 day residency requirement, which means that either the bride or the groom has to be living in India for at least 30 days prior to applying to the local registry office to get married. For foreigners, this is evidenced by a certificate from the local police station.
Since your wife will be here on a tourist visa, you have to convert her visa from a tourist visa to a short visit visa (valid for one year).
Marrying a Bangladeshi as such should not be problem but her getting long term Visa to stay in India after marriage will always be a matter of concern. The reason is that Bangladesh is not in the category of friend countries to India.