In my vocation, architecture, professional liability insurance is useful because in most {all?} US jurisdictions a licensed architect is personally responsible for the work appearing under their seal [Professional Engineers are similarly liable]. So professional liability insurance covers the gap between contractual non-performance for which liability can be passed to a corporate entity such as an LLC or S-corp [in most but not all US jurisdictions] and liability for errors and omissions in the delivery of professional design services.
For programming/software development services it is unlikely [in the US] that there would be any liability which could not be assigned to a corporate entity because there is no licensed profession with regulations prohibiting such assignment. That's not to say that errors and omissions insurance isn't useful, but rather that owing to the lack of an established reasonable standard of care for the practice of programming and a lack of direct personal liability, it's less clear cut.
My recommendation would be to talk with an attorney familar with the software industry regarding your liability.
On the other hand, it is very common for established businesses to require general liability insurance for anyone with whom they contract and such policies are essentially commodity priced starting at a few hundred dollars a year. In many US jurisdictions, established enterprises will also require proof of Worker's Compensation policies.
The good news is that it is relatively easy to purchase insurance and insurance agents produce standardized documents (binders) that document coverage.
Finally, you can roll the cost of insurance into your proposal. It will be helpful to know exact coverage requirements when speaking to an insurance agent, but my experience has been that it is usually the minimum requirement for Worker's Comp and a very basic general liability policy. Anything more expensive prevents them from hiring ordinary services such as janitorial and lawn maintenance.
Good luck.