Recently, when I asked our associate pastor a similar question, he explained to me that Jesus is made present to us in two different ways during mass: the Liturgy of the Word and the Liturgy of the Eucharist. During the Liturgy of the Word, Jesus is present through the Word. In order to focus the church assembly on that spiritual reality, and in order to coordinate our physical bodies with the spiritual realities being made present, he suggested that Lectors bow to the ambo. At all other times (meaning all other times except for during the Liturgy of the Word), one should bow to the altar. Both the ambo and the altar are symbols of Christ, with the altar being uniquely chosen of highest honor.
Our associate pastor did not say that this type of bowing was in the GIRM. But there are some things that are not in the GIRM that are at the discretion of the pastor and the bishop. For instance, some churches have the responsorial psalm sung from the ambo (instead of where ever the musicians are located) in order to physically acknowledge to the assembly that the responsorial psalm is not “just a song” or a musical interlude, but that the Word of God is (still) being proclaimed. As long as there is nothing in the GIRM and the local bishop does not object, I think that pastors have a little leeway in this matter of bowing to the ambo during the Liturgy of the Word or always bowing to the altar at all times. (Please remember, that I am no expert in the GIRM, so someone else may correct what I have just said.)
In anycase, the best thing to do is ask your pastor which he prefers you to do. This makes for a very interesting conversation with others as to “why Catholics do the things they do,” especially in the ways our bodies are meant to reflect the spiritual realities of what is happening at Mass.