If you've placed a thick layer of bark mulch over your flower beds,
how do you go about amending the soil with compost come Springtime?

I don't use bark mulch. I use about 3" of partially decomposed compost (leaves
and grass) as mulch. The worms pull it gradually into the soil. As the mulch
layer thins, I replace it from the compost pile.

Do you scrape aside the mulch, work the soil, then return the mulch?

If I used bark mulch, that is what I would do.

Or do you work the mulch into the soil itself, then apply a fresh
layer?

The bark mulch is high in carbon, but nitrogen-poor. As soil bacteria decompose
the bark mulch, they will use whatever nitrogen is available, depleting the
soil of nitrogen for the plants. Therefore, if you work mulch pellets into the
soil, you should provide a nitrogen source, such as blood or fish fertilizer,
or fresh grass clippings.

Wendy
Wilmington, DE (Zone 7)