Hi,
Definitely, quote per visit.
Don't under-charge just because they give you a hint that they may offer you more work!
You could hint back that you may consider a discount WHEN they supply you with more contracts (in the same area)
You must quote sensibly: your time, your costs, your profit etc.
You can't quote until you do your survey as you don't know how bad they are going to be - or how mucky the tenants are. Also, the state of the carpark and external areas.
Here is an example of a pyramid system that I use. The prices are true and I get the work! but it will depend on the area, council, and if homeowners etc. (Adjust slightly to suit, but don't go too much lower than these!)
You MUST consider the number of floors, as it could mean a lot of steps and hallways to hoover or mop!
2 Flats Apartments: 1 floor 2 floor
£20.00 £25.00
3 Flats Apartments: 1 floor 2 floor 3 floor
£25.00 £30.00 £35.00
4 Flats Apartments: 1 floor 2 floor 3 floor 4 floor
£25.00 £30.00 £40.00 £40.00
5 Flats Apartments: 1 floor 2 floor 3 floor 4 floor 5 floor
£30.00 £35.00 £40.00 £45.00 £50.00
You should now be able to see how it works and keep going up to 9 flats on ? floors.
One last thing: Go and have a look before the official survey. That way, when you get there you will already have an idea of what you are going to quote (that's if you are meeting someone there)
If you don't get the contract, don't always assume it is because of the prices. Put across your professionalism and you stand a good chance. There is plenty more work out there.
Good luck