Zet de tas stevig op de fiets vast.

Because this is a command. Dutch uses the imperative for commands, and for zetten the imperative form is zet.

So:

• zetten = to put / to set
• zet! = put! / set!

In English, we usually leave out the subject in commands too:

• Secure the bag
• Put the bag on the bike

Dutch does the same thing here.

In Dutch commands, the subject is usually left out, just like in English.

So:

• Zet de tas stevig op de fiets vast. = Secure the bag firmly on the bike.

The hidden subject is basically you, but Dutch does not need to say it.

If you want to make it more explicit or more formal, Dutch can add a pronoun, for example:

• Zet jij de tas stevig op de fiets vast.
• Zet u de tas stevig op de fiets vast.

But in a normal instruction, leaving it out is the standard pattern.

Because vastzetten is a separable verb.

The full verb is:

• vastzetten = to fasten / secure / attach firmly

In many sentence patterns, Dutch splits separable verbs into:

• the main verb part at the front: zet
• the particle at the end: vast

So:

• Ik zet de tas vast.
• Zet de tas vast.

This is very common in Dutch. Other examples are:

• aandoen → Doe het licht aan.
• opstaan → Sta op.
• meebrengen → Breng het mee.

So zet ... vast should be understood together as one verb idea: secure / fasten.

Yes. zetten by itself usually means to put, to place, or to set.
But vastzetten means to fasten, to secure, or to attach firmly.

Compare:

• Zet de tas op de fiets.
  = Put the bag on the bike.

• Zet de tas op de fiets vast.
  = Secure the bag on the bike.

So vast adds the idea that the bag should not just be placed there, but made secure.

Stevig means firmly, securely, or tightly, depending on context.

In this sentence it strengthens the idea of fastening:

• vastzetten = secure
• stevig vastzetten = secure firmly / fasten tightly

So stevig tells you how to fasten the bag.

A useful way to feel the difference:

• vastzetten = make it fixed
• stevig vastzetten = make it fixed well and firmly

It is not strictly necessary, but it adds emphasis.

Compare:

• Zet de tas op de fiets vast.
  = Secure the bag on the bike.

• Zet de tas stevig op de fiets vast.
  = Secure the bag firmly on the bike.

So stevig gives extra information about the strength or care of the action. It is a bit like the difference between:

• Tie it on
• Tie it on tightly

Op de fiets literally means on the bike. It focuses on the bag being placed/secured on the bicycle, for example on a rack or carrier.

• op = on
• aan = on/to/attached to

Dutch can sometimes use either one depending on perspective, but here op de fiets is natural because the bag is understood as being carried on the bike.

Very roughly:

• op de fiets = on the bike
• aan de fiets = attached to the bike

In real life, both ideas may overlap, but this sentence chooses the location/result: the bag is secured on the bike.

Because both tas and fiets are de-words in Dutch.

You simply have to learn the article with the noun:

• de tas = the bag
• de fiets = the bicycle

Dutch nouns take either de or het, and there is not always a simple rule you can guess from English. So it is best to memorize nouns together with their article.

In this sentence, stevig naturally comes before the phrase op de fiets vast:

• Zet de tas stevig op de fiets vast.

That sounds normal and clear.

You may also hear slightly different placements in real Dutch, depending on what is being emphasized, but not every possible position sounds equally natural.

For learners, the safest pattern is:

imperative verb + object + adverb + other information + separable particle

So here:

• Zet
  • de tas
    • stevig
      • op de fiets
        • vast

Yes, and you should. That is often the easiest way to understand Dutch separable verbs.

Dictionary form:

• vastzetten

Command form in the sentence:

• Zet ... vast

Other forms:

• Ik zet de tas vast.
• Hij zette de tas vast.
• We hebben de tas vastgezet.

So when learning vocabulary, it is best to store it as vastzetten, not as separate words zetten and vast.

A normal statement would keep the same separable pattern in a main clause:

• Ik zet de tas stevig op de fiets vast.
  = I secure the bag firmly on the bike.

With a modal verb, the word order changes:

• Ik wil de tas stevig op de fiets vastzetten.
  = I want to secure the bag firmly on the bike.

Notice the difference:

• finite main verb in a main clause: zet ... vast
• infinitive at the end: vastzetten

That is a key pattern with separable verbs.

Yes. It sounds like an instruction, for example in a practical situation: loading a bicycle, giving directions, or telling someone to make sure the bag is secure.

A native speaker might also say similar things such as:

• Maak de tas stevig vast op de fiets.
• Zorg dat de tas stevig vastzit op de fiets.

But Zet de tas stevig op de fiets vast is a normal and understandable Dutch command.

Yes, that is the core idea. Vast often means something like:

• fixed
• tight
• secure
• stuck
• not loose

In vastzetten, it contributes the idea of making something firmly fixed in place.

So even though English may translate the whole verb as secure or fasten, the Dutch image is very much put it fixed/tight.

That is why vast appears in many useful Dutch expressions, such as:

• vastmaken = fasten
• vastbinden = tie down
• vastzitten = be stuck / be fixed / be attached

So in this sentence, vast is an important part of the meaning, not just an optional extra word.