Something fundamental to sponsorships: you are receiving advertising money from a company to promote their products and/or services. The company sees sponsorship as an opportunity to reach out and touch a target customer audience. When a NASCAR team goes after corporate sponsorships, they show up with a business plan that describes what events they will attend, the expected media exposure from those events, the demographics of the fans and people watching on TV, and how they will prominently display the sponsor's logo on the car, their transport truck, the driver's suit, EVERYTHING.
If you want to be sponsored, you need to approach the idea with the same thought in mind, because no matter what level you seek funding, the person coughing up the money always wants to know, "What am I getting for my INVESTMENT?" So, if it's a local shop, tell them what local events you will attend, what the expected turn-out for those events is, what the likelihood of generating sales from these events is, and how you are going to prominently display their signage in your booth/pit/stall etc. Show a professional attitude and understand they want to know how sponsoring you will generate sales for them. If you can't do this, it won't matter how cool your car is, you're going to foot the bill yourself.
Stories about sponsors walking up and offering cash with no strings attached are just that: stories. If you really want to do this, you've got to show you understand business and how to generate new business activity for your sponsor. Got it? Now go work on that business plan so you can get someone else to pay for the coolio stuff on your car!