How do I approach store owners about carrying my product?
Most will call to at least say thank you -- and that gives you the opportunity to start to build a rapport with them. If you can customize your product per their audience, let them know.
Can you add value (say with flowers, jewelry or even stuffed animals)? Be sure to mention that as well. If you don't hear back from the people you are targeting, you can follow-up with a phone call and start to build rapport that way.
Just make sure you are targeting the decision maker, and that what you are offering would be a good fit for their own base.
Know also you may be in competition with a current preferred vendor, in which case you'll have to find a way to make your product more attractive (better pricing without necessarily discounting but adding value, service, delivery, options, baskets, etc.).
Again, you simply won't know what works until you start testing approaches, figuring out what works, what doesn't, keeping your winning approaches and killing your losers.
You'll eventually find what works for you, and once you do, you can systemize that to branch out to larger targets, more effectively -- at lower costs. A simple sales letter down the line with your customers' testimonials may be the preferred method of contact, versus a higher-cost sample gift basket.
Remember to diligently track your responses and feedback, as that will be the key to honing in on the system that will eventually work best for you.