Dirt is fairly good black dirt, but very sticky/clumpy (almost like clay sometimes). Good idea to add some sand? Other?
hmmm...sounds like it might be a bit too wet when you are planting, as the soil doesn't sound like it is dry and loose.
Does the planting area drain well?

Hardwood cedar mulch bad when mixed in? When I was younger we'd screen stuff like this out before planting tulips believing that rotten/rotting wood wasn't good. True or not necessary?
I don't think that rotten/rotting wood would be a bad thing and would just scoot it aside to plant, as best I could, and not worry if some got mixed in with the soil. I'm not sure, so hopefully some others will reply.
This year I was helping a very experienced gardener doing some daff digging and replanting. After digging the daffs out, she had me put some soil in the bottom of the hole. Then we added a mixture of potting soil, peat, pine bark 'fines', perlite, alfalfa meal, and worm castings to the hole. Then a cup of perlite was added on top of that, and then the bulbs and the remaining soil, and was lightly tamped down.

The old bulbs get dug up but we just leave them in the dirt as we recover the new bulbs. OK? Should they be taken out?
Assuming they are perennial types, if they have bloomed well for you, I'd just leave them. When the number of blooms decline, I would consider digging them, as they probably need digging and dividing as they have multiplied and the bulbs have become smaller.

Sue

Thanks Sue. The soil is fairly dry and well drained.

Also, no expectation of any flowers from old bulbs. We put in all new bulbs every year. My only concern is any negative consequences from old rotting gushy bulbs.

One thing that did just cross my mind with the old bulbs, btw, is if they'd attract squirrels. Since they're mixed in with the soil they (or parts of them) will be much closer to the surface or even on the surface. Wonder if this would be more attractive to critters and thus they'd start digging and find the new ones. Vs, old bulbs screened out and thus less likely critters will dig down to the new ones below.

I see no point in leaving old rotten or non blooming bulbs in the soil. If your soil is sticky when wet, I would add vegetative matter in the form of finished compost, on a regular schedule to improve the structure or tilth of the soil. I would not add sand, mainly because you could not add enough to make a difference, and would only make it worse. If you are buying new bulbs, and they are not being eaten, you should expect almost 100% growth and bloom. Al