Consider saving costs by having your prototype printed by someone else's 3D printer instead. There are several ways to do this. Here are options in order of affordability:
1) Find local "hacker / maker spaces" (for instance check: https://wiki.hackerspaces.org/List_of_Hacker_Spaces) with a 3D printer. Either join, or make friends with a member(s) that's also interested in your idea.
2) Find a local 3D printing Meetup group.
3) Use 3Dhubs (https://www.3dhubs.com)
4) Use Shapeways (https://www.shapeways.com)
That might significantly reduce your expenses, which will make it easier for you to raise the money needed. To raise the money needed:
1) First describe your idea to friends and family. If they're interested mention that you're looking for early investors.
2) Consider applying to a startup accelerator which will give you both funding (sometimes up to $100k), and resources (many will have a 3D printer you could use, and other tools), as well as mentors and connections to investors.
3) Look into crowdfunding. This requires a decent amount of work, and many times you'll need to have already built some kind of prototype to get people to fund it.
If you'd like to discuss these possibilities in more detail, with respect to your specific idea, let me know,
Do you mean the best way to approach an investor about it, or the best group/person to approach about investing?
If the former I would say go through and show that you have clearly defined goals (what completion looks like, what information you are collecting) along with a clear timeline and action plan of what you will do once the prototyping phase is over. If the individual/group isn't familiar with your industry you may want to highlight or explain how common prototyping is (or how it is used when it is used.)
If the latter, then I would consider starting with the good ol' reliable 3 F's (Friends, Family, Fools.) I have worked with dozens of bootstrapped entrepreneurs and the vast majority of them raise money to get their new ventures going through people they know. It is typically the shortest path for getting the cash you need, and since most first rounds of financing are small relative to the rest of the rounds this may be the perfect time to hit up people who just care about and support what you do. Take my advice though and make sure the investment is formalized and documented and consider using either a straight equity option or if you want to give them some protection you can do a convertible or SAFE style document. If personal networks are out then I would consider crowdfunding or (like many people have done) take out a personal Credit Card and run it down from there. I would suggest that as only a last resort, but I've known many businesses that started with a CC application on a college campus or outside a convenience store (when they used to do that at least haha.)
I've worked with startups who launched with as little as a few thousand dollars from friends/family all the way to seed rounds/series rounds ranging from the hundreds of thousands to millions. If you'd like to discuss seed financing and prototype fundraising/best practices feel free to reach out and schedule a time to connect!
It sounds like you are asking for the money to purchase the equipment, I think there is probably a better solution or two that you could try.
1) How about identifying Universities that could help you prototype and that you could 'borrow' not just 3D printing time from. Potentially getting some smart people, students, facilitators, lecturers, into your project could help grow it faster.
2) Rent time at a 3D printing space. I'm sure you are protective over your idea, but 3D printers are becoming increasingly common and perhaps there's a good way of getting this done locally to you which doesn't require a huge upfront investment.
So say now you have brought down the required investment to create the prototype down from $8k to $500, perhaps that opens up more options - extending an overdraft, the classic friends and family, etc.
I liked someone else's suggestion of doing a Kickstarter or Indiegogo, seems like a good move but they do take alot of effort, planning, and time. Probably more than the initial $500 you could raise yourself through other means.
Good luck. Matt