I'm looking at general liability insurance but the market doesn't seem to comprehend that there might not be a physical location. It's entirely an online business and I work from my laptop remotely with no employees. How can I find an affordable service provider?
You will not get one for online work in that way, or if you do it will be expensive.
You do not need one if you do not have employees, you visit customers at their premises, and your terms and conditions specifically say you are not responsible for any adverse affects or losses incurred with down time, bugs, problems with your online work etc and that the company, not you, take full responsibility for any code or copy they use in their systems. (this is conversational but you get what I mean).
I have never had a single customer balk for even one moment at my terms and conditions that include such get outs as "I do my best and take no responsibility for anything that might happen as a consequence of what I do" (Again you will need better or more formal wording but you get the point).
You may get lots of people say "You do need insurance for this kind of work" but you do not, and in fact I would go as far as saying that it is impossible to get the sort of insurance to cover this. People think they are covered, but they are not.
No person can get injured from you typing code on your laptop. The only thing you need to say is that if your code leads to any problems, it is the customers responsibility for implementing it, or allowing it to be implemented and not fully testing, not yours.