When God forbade idolatry, he forbade service to an idol, or bowing to an idol (Exodus 20:5, 23:24). He did not, then, command bowing to himself. He did command service (Exodus 23:25). But what kind of service does he command?
As a side note on "bowing" or "worship", when we keep the commandments we bow to God in a spiritual sense. When we tell the truth even when a lie would benefit us, we bow to God. When we notice our neighbor's spouse and make up our minds to look the other way, we bow to God. When we decline to discuss another person behind their backs, we bow to God. The kind of "worship" that God requests of us is that we love our neighbors as ourselves.
I think the best way to make my point about what God asks is this: In the Torah (Genesis, Exodus, Leviticus, Numbers, Deuteronomy), the Jews studied carefully and counted each distinct commandment. There are different versions of the list; one can be found here for reference. This list finds 613 distinct commandments, which is a number you will hear often for lists of this type. The list is organized into topics by what the law is most directly about. Here is a summary of how many commands were counted under each topic:
Signs and symbols of the covenant: 5
Prayer and blessings: 4
Love and brotherhood: 14
The poor and unfortunate: 13
Treatment of Gentiles: 6
Marriage, divorce, and family: 23
Forbidden sexual relations: 25
Times and seasons: 36
Dietary laws: 27
Business practices: 14
Employees, servants, and slaves: 19
Vows, oaths, and swearing: 7
Sabbatical and Jubilee Years: 17
The court and judicial procedures: 36
Injuries and damages: 4
Property and property rights: 11
Criminal laws: 7
Punishment and restitution: 24
Idolatry, idolaters, idolatrous practices: 46
Agriculture and animal husbandry: 7
The firstborn: 4
Priests and Levites: 30
Offerings, tithes, and taxes: 24
The Temple, the sanctuary, and sacred objects: 33
Sacrifices and offerings: 102
Ritual purity and impurity: 16
Lepers and leprosy: 4
The king: 7
A few different sections could apply to worship in the way we normally think of it -- though when you look at the individual commands, you are likely to find a command like "Don't offer an animal with a blemish."
But here's the thing: while not every section applies to "worship" as we narrowly define it, every section applies to service. Fair business practices fall under "service to God"; fair treatment of employees likewise. Farming practices fall under "service to God". So does family. So does having a just court system. When we treat our co-workers well, we bow to God just as surely as someone on a prayer mat.
The laws of the Torah are not binding on Christians in the sense that we are not under the Old Covenant from Sinai, but under the New Covenant. Still, we see the writers of the New Testament talking about treatment of family and treatment of servants right along with generosity towards the poor and traditional "worship", all as part of the same topic of how we live as God's people.
When we think of religion in terms of singing hymns and praying and reading Scriptures one day a week, many of us sense that this is completely inadequate. But often, the answer given is to sing hymns and pray and read Scriptures two days a week, or seven days a week. And a great many Christians do read Scriptures and pray seven days a week. While I would not want to discourage anybody from singing, praying, studying, meditating, or any of the good and healthy things we do, it still remains to be said: that is a small part of what God asks of us. That kind of worship is only one topic among many in how we live our Christian lives. No matter how well we fulfill that one thing, it will always leave us with a sense of things undone because it still remains one topic among many that God asks of us.