Answer: I would be concerned about planting in that layer of bark compost. First of all, are you sure it is very well composted? If not, then it may not be a habitable environment for plants. Generally, bark is very slow to decompose, and can be quite acidic. I would also be concerned that your plants wouldn't develop very extensive root systems. The roots would stay concentrated in the bark, and not venture into that hard clay. Then, when you go to water, the water would filter quickly through the compost to the clay surface, and either puddle or drain quickly away before the plants could absorb it.
Is there any way you could make a few raised beds, by mixing some of the clay with the compost, and raking it into flat-topped mounds about 6 to 8" high? Raised beds generally dry out faster than the rest of the garden soil, and these might give you enough lead time to get you started. You could even have a sheet of plastic handy, and cover the early bed (before planting) during heavy rains. (I've done this in my own clay-ey garden.)
I would also recommend a soil test for your clay soil. Often, clay contains a wealth of nutrients--it's just that they are in a form unavailable to plants. By adjusting the soil's pH if necessary, you can release these nutrients. This, and the addition of lots of organic matter (including leaves, grass clippings, compost, manure) can dramatically improve the soil's ability to support your crops. Good luck!
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