Not wanting to sound militant but my policy is the price is for the whole or part of the house. I run 8 weekly, after each clean the invoice is sent with the following date on the invoice, t&c's on each invoice.
We don't txt prior to cleaning, the following date is on the invoice, means they have around 7 weeks and 6 days to forget. I am very clear, responsibility for access is the customers, not mine.
Everyone like to put the responsibility on others, why ? Its easy, I just make it very clear its not mine.
My advice this way is to do what you say.... First time gate/access to not available bill them.
This may not work for you but having a scheduled service does mean if I cannot clean, I lose money on the day and cannot make it up.
I am friendly and polite but I run a business and the vatman wants his money as does the wife and a hundred other people each month.
I schedule the date, customer ensures what they want cleaned is accesable....its a fair system. In the event the customer really wants me to return, I am happy to do so provided time and travel costs can be met.
Again this is not meant to come across all bolshy, merely have learned what works best for me. I have tried the cheeky-chappie 'doormat' approach .....give an inch and they'll take a mile was what I found.
Cheers Dave.