The phrase "putting up bluff" can be translated to a number of synonyms. One of the most common alternatives is "bluffing," which involves deceiving or misleading someone through one's words or actions. Another option is "fake-out," which is similar to bluffing but usually refers to more overtly deceptive behavior. Other possible synonyms for "putting up bluff" include "lying," "pretending," "faking," and "feigning." Ultimately, the exact term one chooses to use will depend on the specific context of the situation and the intended meaning behind the phrasing.