According to Protestants, why was Mary troubled at the greeting of Gabriel?

Well, Mary was likely not only troubled by Gabriel's presence, but also his appearance. Remember, throughout the Bible angels are described as terrifying creatures.

Gabriel then went on to say that the Lord was already with her, and that she was being 'highly favoured'.

In such a situation, it is very unlikely that she will not be burdened with a great responsibility, and indeed she was.

I see from Strong's:

χαριτόω charitóō, khar-ee-to'-o; from G5485; to grace, i.e. indue with special honor:—make accepted, be highly favoured.

This word is only used three times in the New Testament. It is used for Mary, and then twice in Ephesians 1:6--

To the praise of the glory of his grace, wherein he hath made G5487 us accepted G5487 in the beloved.

Perhaps Mary had no context for the word Gabriel used and it puzzled her. Garbriel used a different word with a similar meaning in his next statement:

χάρις cháris, khar'-ece; from G5463; graciousness (as gratifying), of manner or act (abstract or concrete; literal, figurative or spiritual; especially the divine influence upon the heart, and its reflection in the life; including gratitude):—acceptable, benefit, favour, gift, grace(- ious), joy, liberality, pleasure, thank(-s, -worthy).

On http://blueletterbible.com I found this in the outline of Biblical usage for cháris/ G5463:

of the merciful kindness by which God, exerting his holy influence upon souls, turns them to Christ, keeps, strengthens, increases them in Christian faith, knowledge, affection, and kindles them to the exercise of the Christian virtues

With this further explanation of why an angel would be addressing her in an unfamiliar, perhaps unprecidented manner, Mary settled into the conversation. Unlike the priest, Zacharias, who disbelieved Gabriel, Mary only asked for clarification, so that she might understand what was about to happen to her.

Mary humbly submitted herself to God and the role He gave her. She thus was used of God to prepare the Way for all to come into God's favor who believe on her son, the Son of God. As such, she is called blessed, as both Gabriel (text in question above) and Elizabeth greeted her:

And she spake out with a loud voice, and said, Blessed art thou among women, and blessed is the fruit of thy womb. (Luke 1:42)

And as Mary herself declared:

For he hath regarded the low estate of his handmaiden: for, behold, from henceforth all generations shall call me blessed. For he that is mighty hath done to me great things; and holy is his name. And his mercy is on them that fear him from generation to generation. (Luke 1:49-50)

I am unsure of other instances in Scripture where an angel greeted a woman directly. If Mary was familiar with the pentateuch, is it possible that she was frightened by the possibility that the angel was there to do her harm? (Genesis. 6:1-5) Because Gabriel declared that God was with her, I doubt it, but she may have needed a moment to register what He was saying and what it could mean, because his sudden appearance was so startling that he was compelled to tell her "Fear not..."

The Protestant view would not tend toward the level of veneration for Mary as seen in the Roman Catholic Church, but does not discount the importance of her role as an instrument of God for seeing His plan of salvation brought to completion. The incarnation required a mother, and she was selected. She bore the seed of the woman (Genesis 3) to crush the serpent's head, though His heel would be bruised.

Thankful though we are for Mary and her humble submission to God's plan, she is as she called herself, "the handmaid" (servant/bondservant) of the Lord.

Mary could be compared to John the Baptist, who also came to prepare the way for the Lord and announced, "Behold, the Lamb of God, who takes away the sin of the world." John did not elevate himself in God's kingdom, but said, "I must decrease, that He might increase." Jesus said about John:

Truly I tell you, among those born of women there has not risen anyone greater than John the Baptist; yet whoever is least in the kingdom of heaven is greater than he. (Matthew 11:11)

Perhaps it was because John's faith had wavered at that moment, indicating from prison by way of his own disciples, whom he sent with a question, that he was doubting Jesus' identity as Messiah.

Mary and John were both human agents of God's choosing for bringing us Messiah--first into the world by Mary and then into the public eye by John, when he baptized Jesus and declared His identity to the crowds.

We are grateful for them, just as we are grateful for all of the Old Testament prophets and saints (like Esther, whom God used to preserve the remnant from whom the Messiah eventually would descend in the kingly line of Judah). We are grateful for them just as we are grateful for the apostles, and every believer who has participated in faithfully passing along God's Word and the Gospel message of God's grace (cháris/ G5463) by which we are saved. We who believe now, all stand in God's favor, because of she who was greatly favored and chosen for such a special role. (Ephesians 2:8-9)