sizyou no ato de, bouhantouroku to zitensyahoken wo kakuninsuru.

A natural reading is:

しじょう の あとで、ぼうはんとうろく と じてんしゃほけん を かくにんする。

Word readings:

• 試乗 = しじょう
• あとで = あとで
• 防犯登録 = ぼうはんとうろく
• 自転車保険 = じてんしゃほけん
• 確認する = かくにんする

Because 試乗 is being used as a noun here.

試乗 is a suru-noun: it can act like a noun, or it can become a verb with する.

• 試乗する = to test-ride
• 試乗のあとで = after the test ride

So の is linking two nouns:

• 試乗
  • あと
• literally, the after of the test ride

This is very natural in Japanese. You could also say 試乗したあとで, which focuses more clearly on the action having test-ridden.

Here, あとで means after or after that.

In this sentence, the pattern is:

• N の あとで = after N

So:

• 試乗のあとで = after the test ride

The で helps turn あと into an adverbial time expression, so the phrase connects smoothly to the main action that follows.

Both are natural, but they feel slightly different.

• 試乗のあとで

  • treats 試乗 as a noun
  • compact and matter-of-fact
  • common in written instructions, checklists, and business-style language

• 試乗したあとで

  • uses the verb form 試乗した
  • feels a little more explicitly like after someone test-rode it

In many contexts, they mean almost the same thing.

Because と is being used to list two nouns.

• 防犯登録 と 自転車保険 = anti-theft registration and bicycle insurance

This is the standard way to say A and B when naming items.

Because the two nouns are treated as one combined object of 確認する.

So:

• 防犯登録 と 自転車保険 を 確認する

means:

• confirm/check [anti-theft registration and bicycle insurance]

Japanese often uses one particle after the whole list, instead of repeating it after each item.

The dictionary form here gives a neutral, plain statement. Depending on context, it can sound like:

• a general rule
• a procedure step
• a checklist item
• an instruction in a manual or memo style

So this sentence may feel like:

• After the test ride, check the registration and bicycle insurance.

If you wanted a more polite sentence, you might say:

• 確認します
• 確認してください

Yes, the subject is omitted, which is very normal in Japanese.

The sentence does not explicitly say who checks these things. That is usually understood from context. It could be:

• the customer
• the salesperson
• the shop staff
• the person following the procedure

Japanese often leaves out subjects when they are obvious from the situation.

In Japan, 防犯登録 usually refers to the official bicycle anti-theft registration system.

So in context, this probably means checking something like:

• whether the bicycle is properly registered
• whether the registration paperwork is in order
• whether the registration needs to be completed or transferred

It is a fixed, very common term in Japan, especially with bicycles.

Because 自転車保険 is a compound noun.

Japanese often combines nouns directly:

• 自転車
  • 保険 = bicycle insurance

This is very common in formal or practical vocabulary.
You can say 自転車の保険 in some contexts, but 自転車保険 sounds more like the established term or product category.

It is not grammatically required, but it is very natural.

The comma marks a pause after:

• 試乗のあとで、

That makes the sentence easier to read, especially because the opening time phrase is a bit long. Japanese punctuation often helps readability rather than marking strict grammar rules.

No. In normal Japanese writing, this would usually be written without spaces:

試乗のあとで、防犯登録と自転車保険を確認する。

Spaces are often added only in beginner materials to make the sentence easier to read.