English Translation
Will you be so kind as to convey my compliments to her?
Byłbyś is the second person singular conditional of być.
The conditional tense is formed by taking the third person singular past form of the verb, być - był, and adding the appropriate conditional particle, in this case “byś” in the second person singular. This sentence implies that “You” is masculine, if it was feminine it would be “Byłabyś”