I completely understand what you're building and why you're undertaking it. I just can't stress enough the importance of it being welded properly.
If you can essentially weld the bumper from the "backside" also, then I might even suggest you stick weld it (given your limited power sources) and then wire weld the front for aesthetics, grind that flush, and then you can paint it. This way, you'd have better strength, and a fully welded in piece.My opinion,
new welders that opt for wire feeders do so as they are easier to weld with. This is true. But that belies the fact that wire welders are also not as strong as Stick or TIG welding. So you end up defeating yourself somewhat in terms of the objective (strength and safety) to achieve your goal (DIY). This is NOT to say it can't be done properly and fully safely with a wire welder, it can. But that requires someone with experience in welding and the proper gear.
Since you are limited to 110v, I believe that the gauge of steel you are working with is outside the capability of your equipment for a single, full penetration pass, even two-sided. I would never rely on multiple passes in this situation to achieve sufficient strength, only to increase the strength. But multiple passes also create weakness away from the welded seam. So its a Catch-22.
This is all I'm saying. I have no wish to disuade you or discourage you, or demotivate you. Simply to encourage you to understand the importance of what you're undertaking and the steps to having it be safe, affordable, and allow you your DIY pride.
If it fails, quite possibly a lot more than your pride is at risk of injury.