If this is the relevant warranty, then it seems pretty explicit.
https://media.specialized.com/suppor...0009968_r3.pdf
"The original owner shall pay all labor charges connected with the repair or replacement of all parts. Under no circumstances does this Limited Warranty include the cost of travel or shipment to and from an authorized Specialized dealer. Such costs, if any, shall be borne by the original owner."
Also, interestingly, you also don't seemingly have a choice but to use the LBS for the repair if you want the warranteed part (without paying for it):
"Only authorized Specialized dealers are authorized to perform warranty service under this Limited Warranty. Should the bicycle, frameset, or any part be determined by Specialized to be covered by this Limited Warranty, it will be repaired or replaced, at Specialized’s sole option. If your bicycle or frameset is a Specialized Edition (limited edition bicycle or frameset), be aware that an exact warranty replacement may not be possible."