I recently had an issue filling my rental. I emailed off a 3 page pre-screening document to prospects asking them to fill it out prior to our meeting. No one filled it out except for 3 people out of all the tours, however I do think it's a great tool at weeding out who is serious and who isn't, but can scare away potential serious renters too. For example I ask, do you have pets, ever been evicted, length of time at current job, current job, etc. My second time around, I filled my rental and called everyone that inquired, I asked them the same questions on the phone and had better success, rented to my first appointment.
It sounds like your rent my be too high. If it's priced right, calls will come in, and it will rent quick. I had my rental higher last year to test the market, crickets. I also make a point to include everything in the rental, for example my condo includes hot water/heat. I cover the electricity (it's a 498sqft studio), and include parking, and the price becomes that much more attractive. It would be the same a la carte, however it's a great mental trick for marketing.