Canada, like most countries, do not expect tourists to be invited by citizens. (That's something out of the dark ages where tourism was strange and unusual, so foreigners would automatically be suspect and needed to be vouched for by "one of our own").
Neither will they find a statement from a citizen particularly more trustworthy than a statement from the applicant. On the contrary, as a practical matter you can't tell them that she's a genuine tourist who will leave after the trip, because how would you know? All you know is what she's telling you, and she's telling that directly to the visa authorities anyway. Having you as a middleman doesn't help anything.
What she does need a letter from you for is confirming that she will be staying at your place. She will need to provide an itinerary for her trip in the application, including her plans for lodging, and if that says "staying with a friend" on such-and-such dates, they will expect to see corroboration from the host. This holds especially if staying with you is essential for keeping the cost of the trip down to what she can afford, but will be generally expected.
So you need to write a letter -- but make sure it doesn't read like you're trying to vouch for her, which you can't. The letter should state
- Your contact details.
- A brief explanation of your own economic/work circumstances. (You probably don't need to document that, but they will like to hear that you do something other than owning or managing a business that might benefit from employing your friend illegally).
- That you agree that she will stay with her on such-and-such dates.
- (If you live in rented accommodation, evidence that your landlord permits overnight guests. I'm not sure if Canada requires that; the UK does).
- What your relation to the applicant is. (How do you know her? Have you met in person before? What is your motivation for letting her stay in your home? Do you usually offer that to out-of-town visitors of similar acquaintance?) This is also where you should make it explicit whether there's romance involved or not, and if so what your expectations of it is.
- That you plan to travel with her as part of the trip, and include a brief explanation of what's up with that.
Don't bother to make it sound like an invitation addressed to her. "To whom it may concern", speaking about her in third person, is fine.
If your friend is worried that such a letter might still hurt her chances, her best option would be to plan -- and budget! -- for staying at a hotel instead. (That's assuming that you are just friends. If you're actually a couple, that's a material fact that she has to disclose no matter whether or not she's staying with you).