Siempre llevo una libreta pequeña en el bolso para apuntar ideas.

Putting siempre at the beginning gives it a little emphasis, but it still just means always.

So:

• Siempre llevo una libreta... = I always carry a notebook...
• Llevo siempre una libreta... is also possible, but less common in everyday speech.

Starting with siempre is very natural in Spanish.

Spanish often leaves out subject pronouns when they are not needed, because the verb ending already tells you who the subject is.

• llevo = I carry / I take
• so yo is already understood

You could say Yo siempre llevo una libreta pequeña..., but that usually adds emphasis, for example if you want to contrast yourself with someone else.

Here llevo means I carry or I take with me.

It comes from llevar, which often means:

• to carry
• to wear
• to take along

In this sentence, it means you regularly have the notebook with you.

Because llevar usually means to take/carry something along, while traer usually means to bring toward the speaker or toward a destination being focused on.

Here the idea is not bringing the notebook somewhere specific, but carrying it with you in general, so llevar is the natural choice.

Both can be translated as notebook, but they are not always identical.

• libreta often suggests a small notebook or notepad
• cuaderno often suggests a school notebook or a larger notebook

In this sentence, libreta fits very well because it is something small you keep in your bag to jot down ideas.

In Spanish, adjectives usually come after the noun.

So:

• una libreta pequeña = a small notebook

This is the normal word order.
If an adjective comes before the noun, it often adds a more subjective, literary, or emphatic feeling, but here the basic descriptive order is best.

Because the article and adjective have to agree with the noun in gender and number.

• libreta is feminine singular
• so you need una
• and the adjective must also be feminine singular: pequeña

That is why it is:

• una libreta pequeña

not:

• un libreta pequeño

En el bolso means in my bag / in the bag.

A few useful points:

• en = in
• el bolso literally = the bag/handbag

In English, you might say in my bag, but in Spanish it is very common to use the definite article instead of a possessive when the owner is obvious from context.

So en el bolso naturally means something like in my bag here.

Spanish often uses the definite article (el, la, los, las) where English prefers a possessive (my, your, his), especially when the ownership is already clear.

Since the speaker is talking about something they carry, it is obvious whose bag it is.

So both are possible:

• en el bolso = very natural
• en mi bolso = also correct, but slightly more explicit

Para + infinitive is a very common structure meaning in order to or for the purpose of doing something.

So:

• para apuntar ideas = to jot down ideas / in order to write down ideas

This explains the purpose of carrying the notebook.

Other examples:

• Uso gafas para leer. = I use glasses to read.
• Voy al supermercado para comprar pan. = I’m going to the supermarket to buy bread.

Because the sentence is talking about ideas in general, not specific ideas already identified.

So:

• apuntar ideas = write down ideas / jot down ideas in general
• apuntar las ideas would sound more like write down the ideas, meaning specific ideas that have already been mentioned or are known

This is similar to English:

• I write down ideas
• I write down the ideas

Here apuntar means to jot down, to note down, or to write down quickly.

It is very close to anotar, and in many situations they can be used similarly.

A rough difference:

• apuntar often feels a bit like jot down
• anotar often feels a bit more neutral: note down / record

In Spain, apuntar is very common in everyday speech with this meaning.

Yes. Llevo is the present tense of llevar.

In this sentence, the present tense expresses a habit or something the speaker generally does:

• Siempre llevo... = I always carry...

So it does not mean only right now at this exact moment. It describes a regular practice.

Yes, you could. It is grammatically correct.

• una libreta pequeña = the most neutral, standard description
• una pequeña libreta = also correct, but can sound a little more descriptive or stylistically marked

For a learner, una libreta pequeña is the safer default pattern because adjectives usually come after the noun.

Yes, it sounds very natural in Spain.

A couple of details that fit Peninsular Spanish well:

• apuntar ideas is very natural in Spain
• bolso is commonly used for a handbag or everyday bag

If the bag were a backpack, you would usually say mochila instead. So the exact noun can change depending on the kind of bag.