Quiero comprar un billete de ida.

In Spanish, the subject pronoun is often omitted because the verb ending already tells you who the subject is.

• quiero = I want
• The -o ending shows it is yo

So Quiero comprar... is completely natural.
You can say Yo quiero comprar... if you want extra emphasis, contrast, or clarity, but it is not necessary.

Because billete is a masculine noun in Spanish.

• el billete
• un billete

Even though the word ends in -e, that does not automatically make it masculine or feminine. Nouns ending in -e can be either, so you usually have to learn the gender with the noun.

De ida is a fixed expression used for a one-way ticket or journey, literally something like for going / outbound.

Very commonly:

• billete de ida = one-way ticket
• billete de ida y vuelta = return ticket / round-trip ticket

So de ida is not acting like a normal English adjective. Spanish often uses de + noun to describe things in this way.

Because de ida is a set expression. In this context, Spanish does not say de la ida.

You should learn these as chunks:

• billete de ida
• billete de vuelta
• billete de ida y vuelta

Trying to translate word-for-word from English can sound unnatural here. Spanish prefers this fixed pattern.

In Spanish, descriptive information often comes after the noun, especially when it is a phrase.

So:

• un billete de ida
• literally: a ticket of going / outbound
• natural meaning: a one-way ticket

This is very common in Spanish. Compare:

• una taza de café
• una mesa de madera
• un billete de ida

The main noun comes first, and then a de phrase adds more detail.

In Spain, billete is the most natural word for a ticket for transport, such as a train, bus, or plane.

In many parts of Latin America, people often use:

• boleto
• pasaje (in some countries)

So if you are learning Spanish from Spain, billete is the best choice here.

Quiero comprar... is correct and common, but it can sound a little direct depending on the situation.

Softer, more polite options include:

• Quisiera comprar un billete de ida.
• Me gustaría comprar un billete de ida.

These are similar to saying I’d like to buy a one-way ticket rather than I want to buy a one-way ticket.

In many real-life situations, especially at a ticket counter, learners are often taught the softer versions first.

This is a very common Spanish structure:

• a conjugated verb + an infinitive

Here:

• quiero = I want
• comprar = to buy

So quiero comprar means I want to buy.

The second verb stays in the infinitive after verbs like:

• querer
  • infinitive
• poder
  • infinitive
• necesitar
  • infinitive

Examples:

• Quiero comer.
• Puedo entrar.
• Necesito estudiar.

In standard Peninsular Spanish, billete is pronounced approximately bee-YE-te.

A few useful points:

• ll is usually pronounced like y in much of modern Spain
• the te at the end is clearly pronounced
• the stress is on the ye syllable: bi-LLE-te

So a simple learner-friendly guide is:

• billete → bee-YE-te

Depending on the region, the exact sound of ll may vary a little, but bee-YE-te is a good model.

Yes, but in real life they might also shorten it depending on the context.

Natural possibilities include:

• Quiero comprar un billete de ida.
• Un billete de ida, por favor.
• Quisiera un billete de ida.

At a ticket counter, people often use the shorter version because the situation already makes the meaning clear. But your full sentence is perfectly natural and grammatically correct.