How to not awkwardly bow to thurifer during Mass?
Thurification or incensation is an expression of reverence and of prayer, as is signified in Sacred Scripture and rules are actually put down how to perform this liturgical action.
The celebrant should not begin any prayer or commentary until after the incensation has been completed. During the divine office the antiphon for Benedictus or Magnificat should not be repeated until the completion of the incensation.
It also adds several footnotes taken from the 1886 edition of the ceremonial regarding the manner of approaching the bishop, recommending placing three spoonfuls of incense into the thurible, and describing the manner of holding the thurible. For example, footnote 75 states:
"The one incensing holds the top of the censer chain in the left hand, the bottom near the censer in the right hand, so that the censer can be swung back and forth easily. The one incensing should take care to carry out this function with grave and graceful mien, not moving head or body while swinging the censer, holding the left hand with the top of the chains near the chest and moving the right arm back and forth with a measured beat."
To these official documents we may add the indications offered by Monsignor Peter Elliott in his excellent ceremonies book:
"216. The grace and skill of using the thurible depends first of all on how the chains are held when incensing a person or thing. Each person should work out what is most convenient by practice, but an easy method may be proposed. (a) Take the disc and the upper part of the chains in the left hand, letting it rest against the breast. With the right hand, let the chains pass between the index and middle finger. Secure them by the thumb, so that the swinging bowl of the thurible may be directed and controlled easily. (b) With the right hand, bring the bowl in front of the breast. Then raise the right hand to eye level (lower when censing an altar) and move the bowl backwards and forwards towards the person or object, swinging it steadily and smoothly without haste by manipulating the chain. (c) Having completed the required number of swings, lower the bowl once more. Then bring it to your side or return it to the thurifer or deacon.
"217. There are two kinds of swing or "ductus." To make a double swing, the thurible is swung twice at the person or object to be incensed, and then lowered. To make a single swing, it is swung once and then lowered, except when incensing the altar, when these single swings are made continuously as the celebrant walks around it.
"218. The customary rules governing these different forms of incensation are as follow: (a) three double swings are made to incense the Blessed Sacrament, a relic of the Cross, images of Our Lord set up for veneration, the gifts on the altar, the altar cross, the Book of the Gospels, the Easter candle, the celebrant (bishop or priest), a representative of the civil authority officially present at a celebration, the choir, the people and the body of a deceased person; (b) two double swings are made to incense relics or images of Our Lady and the saints set up for veneration. The altar is incensed by single swings. In procession, the thurifer swings the thurible at full length from his right hand. In his left hand he carries the boat against his breast, but his left hand rests flat on the breast if there is a boat bearer.
"219. It is not necessary to let the bowl strike the chains. When incensing a person or the gifts on the altar, the chains should be held about 20 cm. (8 inches) from the bowl; about 30 cm. (12 inches) when incensing the altar and cross. Before and after an incensation, a profound bow is made to the person who is being incensed. While bowing before and after incensing a person, the thurifer lets go of the thurible with the right hand, which is placed on the breast.
"220. In placing incense in the thurible, the amount used ought to be governed by such factors as the size of the church. However, the sign of incense rising is achieved only if the grain or powder is evenly arranged on burning coals. Striking or breaking the coals with the spoon does nothing but dislodge the grains and swinging a thurible which does not produce smoke is ridiculous." - Incensing the Host, Altars, Etc.
Personally, I let the bowl strike the chains. It has a ring to it that is heavenly.
When the thurifer is ready to incense the congregation, he will bow (inclination of the head) to the right and then to the left. In some churches the thurifer does a single bow or inclination of the head. The congregation will respond in kind after the thurifer bows towards them. This is done as an acknowledgment of the prayers of the whole congregation in union with the priest are ascending to heaven!
For the sake of completeness I will offer the description of the double swing found in the Fortescue-O'Connell pre-Vatican II ceremonies book: "The double swing ('ductus duplex') is made by raising the thurible to the level of the face, then swinging it out towards the object or person to be incensed, repeating this outward swing, and then lowering the thurible." - Incensing the Host, Altars, Etc.
This single inclination of the head is only done in recognition of the above facts when the thurifer initially bows towards them. It is done just before being incensed and then immediately after being incensed.
The sweet smell of incense and its rising smoke gave it a kind of natural symbolism. It became the image of something pleasing to God. The rising smoke came to symbolize a person's or people's prayers rising up to God. So in Psalm 141 we have the plea, "Let my prayer come like incense before you."
Early Christians also found symbolic meaning in the use of incense. In the Book of Revelation, for instance, John has a vision of heaven and a kind of heavenly liturgy where the 24 elders worship the lamb that was slain. The elders hold harps and gold bowls filled with incense, "which are the prayers of the holy ones" (5:8). In Revelation 8:3-4 an angel holding a gold censer is given a great quantity of incense to offer and the smoke of the incense goes up before God with prayers.
So, among Christians today, incense has ritual and symbolic meaning. Its sweet aroma symbolizes something pleasing and acceptable being offered to God.
Burning incense is also a sign of reverence and dedication. Incensing the body at a funeral Mass is a sign of reverence for the body that was once the temple of God. In a more solemn liturgy, incensing the Book of Gospels indicates reverence for the word of God and Christ himself who is the Word Incarnate. Incensing the altar shows respect for Christ whom the altar represents and his sacrifice made present upon the altar. Incensing the Easter candle is, again, a sign of reverence for Christ who is the light of the world. Incensing the Blessed Sacrament at Benediction is a sign of adoration and worship given to Christ, truly present upon the altar. It becomes a sign of our prayers rising to heaven. - The Symbolism of Incense