With @36 sq. ft. you can pack in quite a few. Probably 180-200 bulbs planted at least 3" apart. Note that this is not an exact calculation.

When you're planting for a date specific event be sure you have a back up plan - a florist or even the fresh flower carts at Costco or Sam's Club. And protect them from deer and rabbits who love to nip the buds. There are a lot of variables that can impact tulips blooming by a specific date - weather is just one and the type if tulip is another. Do a little web searching for early, midseason and late blooming tulip varieties.

Tulips according to the temp. will either bloom very quickly or slowly, not only could they bloom too fast but they could also open way too slow. I would for sure have a backup plan like was stated.