I don't come right out and ask the budget. Well, sometimes I do, but it's rare.
I not only list a starting price of $4.50, I also do the math & list "the smallest tiered cake we offer serves 35 and is priced starting at $157.50." My first questions are date, reception location, guest count. From there, I ask type of reception and offer size & shapes. Long before the consultation, they know the starting price of a cake for the guest count. I expect them to know if that is within their budget. Example: "For your guest count and reception, I would recommend a cake which serves about 115. I would expect that size cake to range $650-900 depending on the design." My clients should know if that is within the range they can afford.
When it's a groom's cake, I try to be quick about it. Yesterday, I had someone call about a bottle of Grand Marnier. I directed her to my website then to the crown royal bottle I created. I explained that the cake in the photo served about 60 and is priced at $175. When she responded it was just for a few people, I asked the budget. When she replied $100, I gave her several options to fit the budget.
I like knowing the budget up front. It makes my job easier. I do understand that some people think if they reveal the budget, I am going to guide them to a more expensive cake than may otherwise be necessary. Oh...the budget is $500 well then let's trick this cake out!! Nope. I really want to find something that is just right for them. That's hard for people to believe. I try to find a happy medium where I don't waste time (mine or theirs) but also make them feel comfortable.