Reyweld, Flower Man

You can also attract bees by making bee houses for solitary bees. Essentially, you need long thin hollow cylinders in a dry place off the ground. You can use stalks from certain plants (after they die) or drill holes into a thick piece of wood. Having a variety of hole sizes also helps attract different kinds of bees.

Clover is also very good at attracting bees.

As for having a more natural "wild" garden, I'm with Wheat in recommending switching your lawn to not grass. Long grass means ticks, which is awful. Instead, you could get a thyme lawn, or a crawling cedum (if you don't walk on it too often), or something else. Speedwell has taken over most of my backyard lawn, and it doesn't grow taller than a centimeter or so; it flowers in the Summer and brings in lots of bees. However, when you plant it, you won't be able to get rid of it ever again, so...

The purpley-blue flowers are called "Glories of the Snow". I asked a higher up.