Sure you can...but it will cost you.... I've rode my bike to Mexico, had trouble coming back into the U.S... Had a hard time proving that my bike.... was my bike... They wanted to see a title, but like I told the custom officer... Do you have a title for your bicycle???
I had the papers for the motor, but not my bike I got it at a yard sale. But I did register my bike with the National Bike registry and they where able to check thier.
I was told to never take my Bicycle across the border until I prove better ownership....