Very small ones might struggle through a thick mulch but with a normal one they should all be OK.

I actually use wood chip mulch and nothing has any trouble with that so you will be safe enough. I think bulbs like to be well covered and if you see anything struggling you can always pull some of the mulch back.

Putting down a mulch will lower the depth the bulbs are at. This may mean some won't flower the following year as they have to expend their energy getting the leaves to the surface. Snag with a bark mulch is it needs replacing pretty regularly or it simply disappears.

Bark mulch won't prevent weeds, it will only suppress them.

I know that this sounds obvious, but bear in mind that bark used as a weed suppressant is not selective... It won't know the difference between plants that you want to keep and those that you don't.

Weeds have two types of rooting systems. There are those weeds that root under the layer of mulch and those weeds that root on top of the mulch. Once you spread your layer of mulch down, you will in time, be able to see weeds with both those rooting systems in play. Don't worry about the bulbs they will punch their way through just fine. Oh, I left out a third type of weed which is on its way to smothering my hydrangeas.This weed growing within my hydrangias has no roots at all and grows suspended by the plant it rests on with absolutely no contact with the soil at all. I will post pictures of it soon for I would like to get an ID of it.

I should have said I give the area a feed with bonemeal then use newspaper 3 sheets deep before putting the mulch down. I find it very easy to tear the paper to go round the plants which I can see.