The phrase “bearing gifts” is more commonly used. Bearing, the present progressive form of the verb “bear”, means carrying or holding.
The phrase is used in the adage, “Beware Greeks bearing gifts,” which means do not trust your enemies. This is an allusion to the Trojan Horse in Virgil’s epic, the Aenid.
‘Bearing gifts’ also used in the lyrics of the Christmas carol, “We Three Kings” on the 3rd line of the first stanza: “bearing gifts we traverse afar.”
You can use “baring gifts” if you mean ‘revealing’ or ‘divulging’ a gift, following the verb definition of “bare”.