Trey Morita made a voyage from his home in Silver Spring, Maryland, to a dealership in York, Pennsylvania, just to buy a Husqvarna 701 Supermoto. That's how badly he wanted one.

"I just dropped everything and went up there and got it the same day," Morita told CNBC.

However, the software developer lamented that his new Swedish dirt bike, which is converted for street use, is "pretty hard to find. There are a lot of Husqvarna dealerships around. But the bikes usually sell out as soon as they come into stock."

For Husqvarna Motorcycles, the brand with a cult-like following in dirt bikes and supermotos, it's a good problem to have. The company is driving right into the street motorcycle market this year, with plans to release three new street motorcycles: two different Vitpilen (701 and 401), and the Svartpilen 401. Prices start at $6,299 for the 401 series, and $11,999 for the larger engine 701.

The company is owned by KTM AG, which manufactures motorcycles and sports cars. Husqvarna plans to release "a couple thousand" street motorcycles in North America this year, according to Blaine Schuttler, managing director for Husqvarna North America, in an attempt to position itself as a lifestyle brand.

Schuttler said the company will add additional street models to its collection in the future.

In March, the first batch of the motorcycles went on sale in Europe, Australia, New Zealand, Asia and select locations in India. All 200 Husqvarna dealerships in the U.S. and Canada will have the bikes in April, as well as some locations in and around Mexico City.

But it may still be hard to get your hands on one. Husqvarna recently oversold on dealer network orders for the first round of Vitpilen and Svartpilen bikes, according to Schuttler. He said the company has more street bikes arriving later this fall, and expects similar sales momentum.

"People are clamoring to get these new street bikes," Andy Jefferson, media manager at Husqvarna Motorcycles and long-time bike enthusiast, told CNBC. "And we don't see the demand letting up anytime soon. People who want these bikes should get them ASAP."