If you want to permanently import a motorbike into the USA, the first thing is to find out whether it's legally allowed to be there. If the motorcycle is less than 25 years old (From date of manufacture) then it will need to be a model type approved by the National Highways-Traffic Safety Administration (NHTSA). (There's a list of approved cars and bikes which can be imported here.)

If your motorcycle doesn't appear on this list then you can petition the NHTSA to approve the bike for import, however, this is lengthy, costly, there are many forms to fill out and you will need to submit the bike to them for inspection (they will measure things like emissions and assess crash safety). If they decide the bike meets their guidelines they will allow it to be registered with the DMV, otherwise they will either suggest a list of modifications you need to make or outright deny it entry until it is over 25 years old.

If your bike is accepted, the next step is to register it in the state you intend to keep it in. The state will issue you a US licence plate and tag (which needs to be renewed yearly) For this, you may need a US address to register the bike at, and you may also need to provide your spanish licence or convert it to a US licence valid in the state you register it in, and prove you are insured to ride the vehicle. (I'm less sure on this as it varies from state to state).

If the bike is over 25 years old then this process is fairly painless, if it's not then it can be a real pain, but it is still doable.