How would an undergrad fund a conference trip with a single author paper?
Many universities have funds specifically for student travel to conferences. (For example: University of Washington, Wayne State University.) Even if there is no special fund at the university level, your department may be willing to sponsor all or part of the trip. While it's more common in my experience for student travel to be funded directly by their advisor from their research grants, my department has, on occasion, been willing to pitch in (e.g. under circumstances where a student has no advisor, or the advisor can't sponsor the trip.)

Many ACM SIGs (special interest groups) and IEEE societies offer student travel grants including travel costs (up to some amount) for their conferences. Many conferences in computer science arrange student travel grants from a government funding agency and/or industry sponsors. So you might consider submitting to one of those conferences instead, if there is one relevant to your field. There are also special grants for minorities, e.g. this one from ACM's women in computing.

Regardless of the funding issue, I encourage you to find a faculty advisor to give you feedback on your work. (Also, every travel grant I have ever applied for required a letter from an advisor.)