First of all, let's define what sin is according to the Bible. Sin is an immoral act considered to be a transgression of God's law. It is any action, feeling or thoughts that goes against God's standards.
"Everyone who has this hope in Christ keeps himself pure, just as Christ is pure. Whoever sins is guilty of breaking God's law, because sin is a breaking of the law" [1 John 3: 3-4 GNB]
We can confidently say from the Scriptures that killing bugs or any other insects is not a sin. There is no verse in the Bible that prohibit killing of bugs, insects, spiders or other similar creatures.
In fact, the Bible even tells us that the Lord declared some insects cleaned to be eaten. Those that are not fit to be eaten should be eliminated.
"All winged insects that go on all fours are detestable to you. Yet among the winged insects that go on all fours you may eat those that have jointed legs above their feet, with which to hop on the ground. Of them you may eat: the locust of any kind, the bald locust of any kind, and the grasshopper of any kind." [ Leviticus 11: 20-23]
In today's world, most of us do not consider insects as food. When we kill bugs, spiders, it is because they are nuisance in our homes. There's absolutely nothing wrong keeping our homes clean by getting rid of bugs and other similar creatures. Insects are even known to be carriers of diseases.
However, we should avoid killing bugs for no good reason. Every living thing created by God has a purpose. They are also God's creatures, and he has a purpose for them.
One Christian put it this way:
To treat any of God's creatures, no matter how small, with wanton cruelty is a sin. Focusing an a magnifying glass on an ant hill just to see the ants suffer, sprinkling salts on a garden slug just to see it writhe , purposely stepping on any type of bug on the sidewalk just for the morbid satisfaction of it -- these are not the actions of a God-fearing person. [1].
We have all at some point in time killed bugs before. Either intentionally or unintentionally. Even though killing but is not a sin as I said, it is a bad thing to intentionally eliminate them when they possess no threat to you.
Do not take pleasure in killing bugs, but do not hesitate to do it when it is necessary. If you do wind up killing a bug, do so quickly, humanely, and with a minimum of anger or hatred.
In my opinion, God does not see killing bugs as a murder even though animals, just like humans, are His creations too. You can kill a bug if it is threatening you, but you can't kill it for the fun of it.
Some Bible Verses About Insects
Leviticus 11:20-23 GNB
"All winged insects that go on all fours are detestable to you. Yet among the winged insects that go on all fours you may eat those that have jointed legs above their feet, with which to hop on the ground. Of them you may eat: the locust of any kind, the bald locust of any kind, and the grasshopper of any kind."
Luke 12:33 ESV
Sell your possessions, and give it to the needy. Provide yourself with the moneybags that do not grow old, with a treasure in the Heavens that does not fail, where no thief approaches and no moth destroys
Deuteronomy 14:19 ESV
And all winged insects are unclean for you; they shall not be eaten
Ecclesiastes 10:1 ESV
Dead flies make the perfumer's ointment give off a stench; so a little folly outweighs wisdom and honor
Isaiah 50:9
Behold, the Lord God helps me; who will declare me guilty? Behold, all of them wear out like a garment; the moth will eat them up.
Psalm 78:45
He sent among them swarms of flies, which devoured them, and frogs, which destroyed them.
Job 4:19
How much more those who dwell in houses of clay, whose foundations is in the dust, who are crushed like the moth?
Isaiah 59:5
They hatch adders' eggs; they weave the spider's web, he who eats their eggs dies, and from one that is crushed a viper is hatched.
Conclusion
We have learnt from the article that killing bugs is not a sin according to the Christian Bible. Therefore, if you have killed a bug unintentionally, you do not need to worry about it. You have not committed a sin.
However, killing bugs intentionally for the fun of it might be evil in the eyes of God. If a bug possesses no threat to you, you don't have to kill it.
Other related topics
[1] Source