Send a spec of what’s reasonable given the budget and ask for approval before continuing. If you’re worried about bugs increasing the time consider adding a contingency to the budget. Pad everything out a bit. If this runs to multiple cycles, give them deadlines for feedback and push out the schedule if you don’t hear in time.

Also if it’s your first time and you need the cash and experience, you can overdeliver a little. But if nobody is ever unhappy with you then be aware that you probably are overdelivering.