Hugh J. Gorman III recently wrote a piece for the Boston Real Estate Times that is an excellent summary of the process involved in obtaining bonds to release liens on property (usually involving construction projects). While his article is specific to Massachusetts, the process and the requirements are very similar in most every state.
You can expect similar amount of underwriting information being requested, including details on the nature of the dispute, personal/business financial data and collateral will likely be required as the article notes.
The most common variable is the amount of the bond required to discharge the lien and the bond language and attachments required by the party accepting the bond. In some states, like Massachusetts the bond requirement is 100% of the lien, but in other states you can find different requirements such as 110%, 125% or more. This can make a huge difference if you are being required to post collateral for a bond. A strong surety agent can help you negotiate those terms and Cross Surety has handled many of these bonds all over the United States.