TJ Morin

This past season with the Houston Astros, Bregman did pretty well. He hit .260/.315/.453/.768 with 30 doubles, and 26 home runs.
If he came to the Sox, his numbers would probably jump. He would abuse the Green Monster, and probably could get 10-15 more doubles, and maybe a few more home runs.
So what do the Sox need to do to beat out the Tigers? Like Garcia said, just match what the Tigers offer. If the Sox either just add $20 million to whatever the Tigers offer, or match it straight up, Bregman will probably choose Boston. His friend and current Red Sock Walker Buehler has already been recruiting him, so it makes sense.
Hopefully this is what happens, and the Red Sox give Bregman the offer he wants, and the Sox get the right-handed slugger they need.