У меня весной часто бывает аллергия на пыльцу.

In this sentence, Russian uses the very common у + genitive pattern to express that someone has something or experiences something.

So у меня literally means at me, but in natural English it often corresponds to I have or I get.

That is why Russian says:

• У меня аллергия = I have an allergy
• У меня болит голова = I have a headache
• У меня температура = I have a fever

Using я would require a different sentence structure. Russian usually does not say я имею аллергию in normal everyday speech.

Меня is the genitive singular form of я.

It is genitive because the preposition у requires the genitive in this possession/experience construction:

• у меня
• у тебя
• у него
• у неё

So in У меня весной часто бывает аллергия на пыльцу, меня is genitive because of у.

The grammatical subject is аллергия.

You can tell because the verb is бывает, which is 3rd person singular, and it agrees with аллергия, a singular feminine noun.

So structurally, the sentence is closer to:

• At me, in spring, often occurs allergy to pollen

In other words:

• у меня = experiencer/possessor
• аллергия = grammatical subject
• бывает = agrees with аллергия

Бывает comes from бывать, and here it means something like:

• happens
• occurs
• comes up
• I get

It is especially natural when talking about something that happens repeatedly or from time to time.

So часто бывает gives the idea of often happens or often occurs.

That makes it a good match for seasonal allergy, because the sentence is not just stating a permanent fact in the most neutral way; it is describing a recurring experience.

In modern Russian, present-tense есть is often omitted altogether in simple statements.

So:

• У меня аллергия на пыльцу = I have a pollen allergy

But бывает adds an important nuance: it suggests something that occurs recurrently.

Compare:

• У меня аллергия на пыльцу = I have a pollen allergy / I’m allergic to pollen
• У меня часто бывает аллергия на пыльцу = I often get allergy symptoms from pollen / I often have pollen allergy in spring

So бывает is not just a substitute for есть. It adds the idea of repeated occurrence.

Yes, бывает is a present-tense form, but it comes from бывать, not directly from быть.

• быть = to be
• бывать = to happen / to occur / to be at times / to occur repeatedly

In this sentence, бывает has a habitual meaning: something that happens from time to time, or often.

That is why часто бывает sounds very natural together.

Весной is the instrumental singular of весна, and seasons are very often used in the instrumental with no preposition to mean in spring, in summer, and so on.

So:

• весной = in spring
• летом = in summer
• осенью = in autumn
• зимой = in winter

This is a very common time expression in Russian.

So весной here simply means in spring.

Пыльцу is accusative singular of пыльца.

The reason is that Russian normally uses the fixed pattern:

• аллергия на + accusative

So:

• аллергия на пыльцу = allergy to pollen
• аллергия на орехи = allergy to nuts
• аллергия на кошек = allergy to cats
• аллергия на молоко = allergy to milk

This is just the standard Russian way to express what someone is allergic to.

Usually, with the noun аллергия, the normal pattern is на + accusative:

• аллергия на пыльцу

Using от пыльцы would sound less standard in this exact phrase. От is more natural when talking about a reaction or symptoms caused by something, for example:

• Я чихаю от пыльцы = I sneeze because of pollen

So with аллергия, stick with на.

Yes, the word order can change, because Russian word order is fairly flexible.

The original sentence is natural:

• У меня весной часто бывает аллергия на пыльцу.

But these are also possible:

• Весной у меня часто бывает аллергия на пыльцу.
• У меня часто бывает аллергия на пыльцу весной.

The difference is mainly emphasis and flow, not basic meaning.

A version starting with Весной is often especially natural, because it sets the time frame first:

• Весной у меня часто бывает аллергия на пыльцу.

Yes, but the nuance changes.

If you say:

• У меня весной аллергия на пыльцу

that sounds more like a general fact: I have a pollen allergy in spring.

If you say:

• У меня весной бывает аллергия на пыльцу

that suggests it occurs in spring, perhaps not every single time, but as a recurring thing.

If you say:

• У меня весной часто бывает аллергия на пыльцу

you make the repeated nature even clearer: it often happens.

So часто бывает is there to emphasize habitual recurrence.

Yes, it is natural Russian.

A native speaker might also say:

• Весной у меня часто бывает аллергия на пыльцу.

This version may sound slightly more natural in many contexts because Russian often puts the time expression first.

But your original sentence is absolutely normal and correct.