Disregarding the fact that getting an abortion should not be a crime, in general, traveling to commit a crime is not a right.
This puts the cart before the horse in important ways. First, the government cannot (except with probable cause) treat you as if you are presumptively guilty of a crime until it's done with the due process of proving it. Is being female and in a car probable cause?
Second, is it a crime to travel somewhere to do a thing that's legal there?
Here, both the 4th Amendment and the Commerce Clause of the constitution (in theory at least) constrain the state and officers of said state- the 4th protects privacy of person, home, effects, and papers and requires a warrant to search those things, and the commerce clause implicitly forbids states from enacting laws that effectively regulate commerce in another state.
In theory, under the Commerce Clause states are not authorized to enact law to criminalize that which is legal in other states- that authority is reserved to congress. If that's the case, the phrase 'traveling to commit a crime is not a right' is missing an important piece- the crime part. If abortion is a crime here and the person is traveling there to do a thing that's legal there, this isn't a crime.