The funny thing about a budget is that you can sometimes create a budget out of thin air even when there wasn't one. People tend to often find money for what they want and not have money for what they don’t want. While finding out what budget they have is a nice piece of information to have, be careful that it doesn't end up being used to close the door to your products or services.
For example, if you ask someone what their budget is and they reply "I don't have money for that", where do you go from there?
What you want to sell them is on the value that your services will bring to them, to their business, to their clients and to their life.
Then you are no longer exchanging dollars for hours but dollars for value. They will no longer see your cost as money going out of their pocket but time they gained by having you as part of their business support circle, as extra time now available to focus on their clients, as quality time available to spend with their family and of course to avoid the pain of figuring out and doing the work themselves.
Of course, if it sounds like they have had other people before you in the same role, you could simply ask them what their budget is. Just be warned that the answer it might close the door to continuing the conversation. If this happens, quickly switch to comparing the value that they got and what they could be getting from you. After all, of they are asking about your services and no longer have the previous person, chances are that they weren't happy with the value they were getting before.