I know the female version of proprietor can be called as proprietress or proprietrix.
But I want to know whether a female proprietor can also be called a proprietor? Or does proprietor only indicate a male business person?
Most people will have no problem with calling her proprietor.
Actually some people will reject the idea that you need a female form of the word anyway. Why would the word proprietor only be applicable to a man, and not simply to a person?
So actually, calling her a proprietor is the safer and better option. Don't use an -ess or -ix version.
Legally it might even be a problem. What is a proprietor of a company is a party in a contract, and the company is sold to a proprietor of the opposite sex. Does that mean all contracts in which the proprietor was a party are null and void until the sex has changed?
A quick check seems to confirm we are talking about India. I know that there are accounts (and possibly other services) that are available to one sex only. If this is such a case, it might be appropriate to explicitly indicate the sex of the proprietor. While many people (including me) will balk at the sexist implications of this, it is always wise to pick your battles. And when you need the services the bank can offer you, it might not be a battle worth the fight...
In recent years there has been a push back on this concept of the -or suffix.
For years, female actors were called actresses. And, then the term began to fall out of favor with many female participants in the performing arts preferring actor or female actor. Here is a nice article on the subject..
In the case of actor/actress the word actress may have carried some implications about the woman's morality, suitability for society, etc. (And, I think proprietress may have had some similar connotations of being a Madam in a brothel.)
But, in general, I believe the focus of the past decades has been equality. [I am trying to avoid banal descriptions like the "Women's Liberation Movement" here.] And, for many people, if two people are performing the same function there is no reason to delineate the sex of the person in the name of the occupation.
So, I would say, your bank manager's sense of propriety aside, feel free to use either to describe yourself.
As @David points out, there's still scope for flexibility with "unisex" use of some terms (actor being a prime case in point). But it's not really even an issue with proprietor...
Click on the chart itself to see that I really did include "she is the proprietress" as a search string - it just doesn't occur often enough to graph. The Google Books "guesstimate" for she is the proprietor is 48,400. With ...proprietress it's 3,880, and ...proprietrix occurs just 8 times . Most of the latter two are from sources decades if not centuries old. They're not used much at all today.