Thanks for the responses, both of you. I absolutely suck at math, and don't know the actual numbers to substitute in the equation Done by Forty provided. I've only had the car for a year and a half so "average" maintenance costs are a bit of a mystery. My fuel gauge is not terribly accurate, it appears (for example, when I fill up the tank I get about 100 km before the needle comes down to the full line, but the last 1/4 tank of gas appears to evaporate overnight!) And I've only been working to modify my driving for a couple of months, so I don't have any idea of how many mpg or km/l I'm actually getting. In fact, the only thing I can say for sure is that I filled up the tank when it was $1.17 (approx) per litre. I've heard people throw around a number that the IRS allows for mileage purposes - 50 cents or so? What is that supposed to take into account? I assume that my employers amount of 52 cents per km is intended to cover something similar (although there are of course differences between miles and km, and price of gas in Canada vs US).
What I do know is that by far my biggest expense for the car is my insurance cost, and that is a relatively fixed cost regardless of how much I drive (of course insurance is impacted by amount that you drive, but this one trip out of the city isn't going to make a big difference.) That's really what got me started thinking about being the one to drive - because if mileage reimbursement is supposed to help cover the cost of insurance and maintenance then I'd like to take advantage of that.
In terms of car pooling with my friend and other co-workers, it's probably only realistic with my one friend who happens to live near me. We are all clergy, each person working at separate churches, and mostly living near those churches. That also means that we are each eligible for reimbursement, but none of us would submit if we weren't the one driving, or, so that no one church bears the cost for both people getting there, we would each submit for part of the trip and then hand the money off to the person who actually does the driving. I agree it doesn't make sense for us to drive separately, which is why I would definitely either ride with her or drive her.
I've sent the friend an e-mail letting her know what I'm thinking and asking if she'd be ok with me doing the driving. As a bonus, I realized that this week we're both attending another event that's being held at the church where I work. I don't get mileage reimbursement for going to my own location, so I've actually asked her if I can ride with her that day! So regardless of what happens next week, that's 20+ km less that I'll drive this month :-)