We're headed in that direction and consulting services as well.
Really all time-based billing suffers from an inherent conflict of interest. The supplier controls the inventory. They control the amount, price, and quality of inventory consumed while the buyer has little if any data.
For your own situation, when you ask your CPA for a budget follow up with a request for a fixed fee proposal. If the two numbers differ significantly, ask for an explanation of why costs might exceed budget. That at least gives you a starting point. You could ask for time sheets, but if it's a one-person show, there may not be any time sheets. Fixed fee is the answer.