I have to say that the type of client you describe have been an asset to my business over the years
Do you normally work for this type of customer?
Here's how I see it. Someone with 50k in the bank who lives in a 4 bed detached house can hide it, they blend in to the sales reps and middle managers of this world. When you turn up on the doorstep they know you don't have £££ signs flashing up so they don't feel like you're there to rip them off. They're not so defensive.
However, these people with the mansion house and the selection of luxury cars outside cannot hide the fact that they've got a few quid. They must go through life constantly battling against businesses and tradesmen who think that because this client is rich they can fleece them for every last penny.
Who has the right to do that?!! Nobody, but of course some try it on so they have to put up barriers initially. Her "don't want to pay too much" is an opening gambit, she's being cautious and sounding you out, it doesn't mean she won't pay your price if you sell it to her effectively.
These customers are more than willing to pay a decent amount for someone to do a quality job for them, but here's the crunch... once you've gained their hard-earned trust you have a constant source of business from them!!
Too many people in business can't see past the end of their nose. Just want to make it clear this is NOT a personal dig at you Neil, I'm not really referring to your words but many people have similar misconceptions about these sort of client and it boggles my mind!