Thanks for your wonderful question. Yes, the Holy Sacrifice of the Mass is the highest, most solemn, form of worship we have as Catholics. As such, it is due the utmost reverence and respect. All the more is such reverence and respect due to the Most Blessed Sacrament. Officially, the Church says this:
When receiving Holy Communion, the communicant bows his or her head before the Sacrament as a gesture of reverence and receives the Body of the Lord from the minister. The consecrated host may be received either on the tongue or in the hand, at the discretion of each communicant. When Holy Communion is received under both kinds, the sign of reverence is also made before receiving the Precious Blood. —General Instructions of the Roman Missal, #160
So, it seems to me that you are quite correct that the sign of reverence should be given before receiving the Sacrament. For purposes of practicality and efficiency, this has evolved, so to speak, into the habit that most people make the prescribed bow while the person in front of him or her is receiving Holy Communion. I think the key thing in either practice is that the individual’s heart is properly disposed to receiving the Body and Blood of our Lord.
Some questions we might ask ourselves in order to ensure a proper disposition to receive the Body and Blood of the Lord might be:
Am I in a state of grace? Am I conscious of any unconfessed serious (mortal) sin?
Have I kept the prescribed one hour Communion fast?
Have I reflected on the fact that Jesus Christ is truly present, Body, Blood, Soul, and Divinity, in the host that I am about to receive? Have I reflected on how remarkable a gift that truly is?
Thank you for your diligence in striving to make your own reception of our Lord’s Body and Blood all the more meaningful.