A recent video interview features a rabbi claiming that the root of בְּשׂוֹרָה is בְּשַׂר (flesh).  The standard Hebrew reference volumes do not connect it this way (suggesting a separate root with the same consonantal spelling — בָּשַׂר: to bear tidings)… but it is an interesting premise.  Consider this possible connection in light of Yeshua’s statement, “This is my body [בְּשַׂר in Hebrew or בָּשָׂר in Aramaic; flesh]; take and eat [proclaim the בְּשׂוֹרָה?] in remembrance of Me.”