The rubber safety tiles only need a level base - there's no need for decking or anything as ridiculous as that! If the existing bitmac is reasonably level, then the tiles could sit directly on top.
There is also a wet-pour rubber-like surfacing that can be used on uneven surfaces, but that's usually a bit more expensive than the self-fit tiles.
I recently saw some interlocking crumb-rubber paving blocks, only around 25mm thick, that can be used for playgrounds and the like. They were selling for around 30 quid per square metre, plus the VAT, and then there's the installation cost.
However, I'm sure I was talking to one of the crumb-rubber tile suppliers at GLEE last year and they were offering a basic, black, nowt-fancy, safety tile system at only 22 quid per square metre, including the fitting glue.
There are no cheaper alternatives, unless you accept a loose-fill, such as play bark or crumb-rubber, and all the problems that come with them.
Do you know the name of the product offered at your local BM?