If you are running a legitimate business as a companion (paying your taxes, GST etc) then I think accepting credit cards is a great idea. Over 85% of my income is from credit card transactions, about 10% in interac transfers, and only about 5% in cash.
With that said, my income didn't really change when I began accepting credit cards. It just made my suitors lives a bit easier, and mine as well, since I didn't have to run to make bank drops every day.
It's much more convenient for gentlemen to use (and explain) credit card transactions than large cash withdrawals. We are almost a cashless society, and busy people don't have the time or desire to hit up banks to get paper. This may be different if your rates are in the $200-$300 range, but I think once you get over $300, it becomes much more difficult to carry a pocket full of cash.....especially if you are looking to book multiple hours.
Just make sure your business name is discreet and industry neutral. It should never raise any flags with an accountant, partner, friend or anybody else who may see a credit card statement. However, DO NOT WRITE IT OFF! It doesn't matter how clever the business name is....this is not a deductible expense in Canada for any reason. It doesn't matter what the business is registered as - if a gent gets audited, falsifying paperwork to be in alignment with what your business is registered as is going turn into all sorts of fraud. And encouraging (or not discouraging) your clients to write it off puts you in hot water too.