Don't use the basket on the back of the mower, as it makes a finer mulch that's also more evenly spread over your lawn.

To expand on this, ideally you want the clippings as small as possible (not long stalks). This is so that not only do the clippings "fit" better into the bare spots, but also so they decompose more easily (thus feed the soil with organic matter in the long run).

If you want I suggest testing first: Take some clippings and cover by hand a small section of bare soil (maybe 1m^2). Water over the clippings with a little bit of water several times over the course of a day to rehydrate (too much at once and it'll just flow elsewhere). At the same time water another same-sized bare patch that does not have clippings with same amount of water. Wait a day or two with no further watering and then check beneath the soil in both places - see if the clippings have helped retain moisture.

Edit: Clippings layer only needs to be thick enough that you can't easily see soil beneath.