you need to bury the wire around the bulbs and leave it there. I think tulips are every bit as tempting to squirrels as are crocuses. Try spraying with Ropel (on the bulb when planting) and then around the area after that...or some type of deer off product. You can certainly plant any perennial around/near the bulbs.

I have always protected most plantings with 2" wire mesh, i.e.,"chicken wire", by covering the planting area with it and pinning it down with "hairpins', made of heavy gauge wire. In raised beds, it is covered with mulch and forgotten. In lawn areas, where Crocus and Rockgarden Iris reticulata are planted, I usually remove it after the first season. Once the soil has settled and compacted around the bulbs, the rodents usually lose interest. If you plant perennials among the bulbs, just cut an X with wire cutters, bend the wire back and plant. You can then bend the cut edges back over the planted area, leaving enough space for the plant. I always bend the cut edges upward near the new planting to discourage nosy animals.
I grow thousands of plants and since part of my garden is heavily wooded, I have vastly more than my share of Squirrels and Chipmunks, so I purchase the wire mesh in 4' x 100' rolls, which will last about 2 seasons.
I also trap and relocate the critters to distant areas, which is a never ending endeavour!
Good luck!
Rb