i never "offer" one time mows.
if someone calls up and wants one i will take it on if my schedule is not already full. the only time that usually happens in at the end of summer when there is a lack of rain. spring, most of summer and fall are pretty booked for me.
depending on how long the grass is will depend on the price.
location has no affect. i don't care if your right next door to an exsisting client, if my schedule is full it's full.
in my neck of the woods one time cuts are usually those who can't or don't want to afford a regular lawn service. most of the time the grass hasn't been cut in months. they will either get you to knock it down once and try and not pay and then call someone else when it needs it again or they will just call you every 3 months or when they feel like it.
i had this couple do that to me earlier this year. guy called me up and wanted an estimate. came out and looked and it hadn't been cut in like 3 months. gave him a price and he didn't realize grass cutting was that "expensive" he said. but agreed so i cut it, invoiced him. he didn't pay. 2 months later his wife called and wanted me to come back out and cut the grass again. i said not until you pay the previous invoice and the new service dated ahead. they paid it ahead and i cut it. hadn't been cut since the last time i cut it. then again 2 months down the road called and wanted it cut again. i didn't call them back that time.
i'm not gonna show up every 2 months or when you feel like it and spend all that time getting the lawn in shape only to have you let it go inbetween my services.