The calculation for my business travel: (60km one way to airport)
If I am leaving for 2 full days or more (e.g., pay parking for 2 full days +), it is break even for the company to pay for the taxi.
Taxi at $60 x 2 ways = $120
versus
$60 (approximately) paid mileage to me plus $30x2+ days airport parking. (expenses)
The Taxi is the most convenient, and reduces wear and tear on my car. Why? Either parking at airport in extreme sun or frozen snow for extended time, plus the airport dust "fall out" is a bit tough on the car. Greatly reduces my annual mileage. I am often too tired to drive after a long return flight...
I also prefer the convenience of being able to check my email / make calls, while on the way to the airport, and the time saved from "at the door" drop off versus the airport parking shuttles.
HOWEVER, Financially...
The cost is better to me to have the mileage, if the company pays for the parking... BUT, company policy is to use the most cost efficient method to the company, so they can balk at long mileage charges, and I get reduced $/mile when the annual reimbursement is over a minimal amount.
To your question..
Let's assume that 100 mile taxi would be $120+ x 2 directions = $240 (No money to you, or just 2% back on cash back cc)
or
Parking for 1 week (7 nights) is $25 x 8 days, plus $110 mileage = $310 ($110 to you, of which 1/2 is cost for wear and tear and fuel, and more for depreciation mileage, plus 2% cash back on fuel and parking on cc rebate)
or
Rent a car one way, drop off at airport $60 (?)x 2 days + Fuel $50 = $170 can you even rent locally easily. No money to you, get two transactions, of which you get a free day ($60 value) every 7 or so trips. Do you have a need for a rental car? Plus again, 2% cash back on your cc.
OR (new option)
Shuttle van (shared car pool van door to door to airport).. $70 one way x 2...
This is the best option for savings and convenience, and my go to when the company would not pay for taxi.
If your company allows you to pay for expenses using your own credit card, and you are playing the bonus miles game, then you may be able to use company expenses as a form of manufactured spending, to get your sign up bonuses. In that case, you need to look for how to maximize out your approved charges to the company. I would definitely try the TAXI option in this case, and show how it is cheaper for the company than you driving. Your benefit is $240 manufactured spend on the bonus CC, versus $60 in your pocket for net mileage.... Is that enough to make a difference to you?