"...However I assume that the shower tray would then start filling with water every time the bath was emptied due to the higher level of water in the bath..."
I have a similar situation relating to a bath and bidet. OK, the bidet outlet is a bit higher than that of a shower tray, but the bath water level is regularly way above that of the bidet outlet and I've never had a problem with bath water backfilling the bidet.
I should imagine that the key factors are the relative flow capacities of the bath outlet and the length of pipe that leaves your bathroom. Let's take an extreme example... If you had a bath and shower tray close together connected to a very long run of shared outlet pipe (such that the length affected the flow rate), then you might expect the bath to fill the shower tray unless you took steps to restrict the flow from the bath (such that it couldn't deliver more water than the long pipe run could cope with). In an even more extreme example imagine if the flow in the common part of the pipe is blocked. In that situation the bath water WILL flow back into the shower tray until it reaches a common level - something you obviously want to avoid. At the other extreme, imagine a bath and shower tray connected to a very short common pipe run... As that pipe run gets shorter and shorter, it has less and less effect on the flow. Eventually the flow rate is limited by the bath outlet and trap, at which point it becomes impossible for water to backfill the shower tray.
In my limited experience, provided that you use swept joints the right way round and the bath and shower don't share a long common length of pipe, and you don't encounter any blockages in the common part of the pipe run, there isn't a problem. If anything, I've found that the emptying of the bath creates suction at the bidet and sink such that there's a tendency for the water in their traps to be sucked out by the flow from the bath. Of course, although I haven't found this a problem in practice, this may be something you would want to avoid - and there's probably a regulation somewhere that relates to the effectiveness of traps and maybe even prohibits this sort of installation.
If you really don't want two separate drains I'd be inclined to test it. Tee into the existing pipe with a trap and outlet at the position where the shower tray is to be sited, fill up tha bath and see what happens.
Just my experience... and if you haven't already guessed, I'm not a plumber so you may want to disregard what I've said!
Mike