There are a couple things you can do to ease a bride's reservations about giving you a deposit. First, a detailed and formalized contract should help them feel more at ease. It shows that you're serious about what you do and that you plan to stick around. Also, it makes thwm feel like they have a leg to zstand on if your business were to ever go under. You may also want to identify how your competitors handle the deposit situation...call them even to see what their policies are so that you can be competitive. Be clear about any refund policies so that there are no misunderstandings. You may even want to consider a slightly lower deposit compared to competitors. That will enable you to say "Well my competition usually requires a 50% deposit but I am willing to accept X.". This does two things...it reduces their risk relative to the competition. Also, this has the potential to help your cash flows as you receive a larger portion of your revenues closer to the day of service. Hope this helps.
To start make sure to have an air tight solid contract approved and reviewed by a lawyer. The contract details should have clear terms and conditions, cancellation policy, payment policy, just in case you cant make it policies and procedures if you should get sick. Be sure to review with the client, explain why you ask for a deposit, answer any questions and send the client home with a copy. You have to present yourself as a serious business owner, and not someone fly by night photographer. To get the client to trust you and your services BE TRANSPARENT in everything from A to Z.