Riempio la vasca con acqua calda.

Riempio is the 1st person singular, present indicative of riempire (to fill).

So it corresponds to I fill or I’m filling, depending on context.

• riempio = I fill / I am filling
• infinitive: riempire = to fill

Because Italian often omits the subject pronoun when it is already clear from the verb ending.

• riempio already tells you the subject is I
• Io riempio la vasca... is possible, but it adds emphasis, contrast, or clarity

So:

• Riempio la vasca... = neutral, normal Italian
• Io riempio la vasca... = I fill the tub (maybe not someone else)

In Italian, singular count nouns usually need an article or another determiner.

So vasca by itself would usually sound incomplete here.
La vasca means the tub / the bathtub, referring to a specific one.

Italian uses definite articles more often than English does, so this is very normal.

Vasca can mean several things depending on context: tub, tank, basin, or bathtub.

In this sentence, because you are filling it with hot water, the most natural meaning is bathtub.

So here la vasca is best understood as the bathtub.

Con means with, and here it introduces the substance being used to fill the tub.

So:

• con acqua calda = with hot water

This is a very natural way to express what you are filling it with.

You may also see riempire used with di / d’ in other sentences, for example riempire la vasca d’acqua. That structure is also common. Here, con simply works well and sounds natural.

Because acqua is a mass noun here, used in a general sense.

So:

• con acqua calda = with hot water, generally
• con l’acqua calda = with the hot water, meaning some specific hot water already identified in the conversation

After prepositions, Italian often leaves out the article with uncountable nouns when speaking generally.

Because calda must agree with acqua, and acqua is feminine singular.

So:

• acqua = feminine singular
• adjective must match it
• therefore: acqua calda

Not:

• acqua caldo

Because acqua is feminine, but la becomes l’ before a vowel.

So:

• la acqua → l’acqua

That does not make the noun masculine. It is still feminine, which is why the adjective is still feminine too:

• l’acqua calda
• quest’acqua fredda

not:

• l’acqua caldo
• questo acqua

It can mean either one, depending on context.

Italian present tense often covers both:

• I fill the tub with hot water
• I’m filling the tub with hot water

If you want to make the ongoing action especially clear, Italian can use:

• Sto riempiendo la vasca con acqua calda = I’m filling the tub with hot water

But the simple present riempio is completely normal.

Yes, absolutely. It is grammatically correct.

The difference is mainly one of style and emphasis:

• Riempio la vasca con acqua calda. = neutral, natural
• Io riempio la vasca con acqua calda. = emphasizes I

So the version without io is usually the more natural everyday choice unless you want contrast or emphasis.