If the trips you described would be deductible if you were
using your own vehicle, then they can be deducted.
If you have a qualified home office that serves as your
principal place of business, then trips from home to other business locations
would be deductible. Otherwise, trips
from home to a business location are considered commuting expenses and are not
deductible.
Trips between business locations are deductible.
See IRS Publication 463 for more guidance about deductible
transportation costs: https://www.irs.gov/pub/irs-pdf/p463.pdf
Also, click on the picture below for a chart that may be
helpful.