Toplantı biter bitmez sana mesaj atacağım.

It means as soon as it ends or the moment it ends.

This is a very common Turkish pattern:

verb + positive aorist + same verb + negative aorist

So here:

• biter = it ends
• bitmez = literally it doesn’t end

But together, biter bitmez means as soon as it ends.

Other common examples:

• gelir gelmez = as soon as he/she comes
• duyar duymaz = as soon as he/she hears
• varır varmaz = as soon as he/she arrives

By itself, bitmez really does mean it doesn’t end / it won’t end.

But in the fixed pattern biter bitmez, it does not create a negative meaning. The whole expression works like a set structure meaning immediately when it happens.

So you should learn biter bitmez as one grammatical pattern, not as a literal combination of ends + doesn’t end.

Both are possible, but they are not exactly the same.

• Toplantı bitince sana mesaj atacağım = When the meeting ends, I’ll message you
• Toplantı biter bitmez sana mesaj atacağım = As soon as the meeting ends, I’ll message you

So biter bitmez is stronger and emphasizes immediacy.

If the speaker wants to say right away, this pattern is a very natural choice.

Because toplantı is the subject of biter.

The meeting is the thing that ends, so it stays in its basic form:

• toplantı = the meeting

You would use toplantıyı only if meeting were a direct object, but that is not the case here.

Sana is the dative form of sen:

• sen = you
• sana = to you

With mesaj atmak, the person receiving the message is marked with the dative case:

• sana mesaj atmak = to send you a message / to text you

So this works a bit like English to you, even though English often just says message you.

Yes, atmak literally means to throw, but in modern Turkish mesaj atmak is a very common expression meaning:

• to send a message
• to text
• to message someone

So this is an idiomatic everyday expression.

A more formal or more literal alternative is:

• mesaj göndermek = to send a message

But mesaj atmak is extremely natural in conversation.

Atacağım comes from:

• at- = send / throw
• -acak / -ecek = future tense
• -ım / -im / -um / -üm = I

So:

• at-
• atacak
• atacağım = I will send

The k changes to ğ before the personal ending, which is why you get atacağım, not atacakım.

So the full meaning is I will send.

Turkish often leaves out subject pronouns when they are clear from the verb ending.

In atacağım, the ending already tells you the subject is I.

So:

• mesaj atacağım = I will send a message

You can add ben if you want emphasis:

• Ben sana mesaj atacağım = I will message you
  maybe with contrast or emphasis

But in a normal sentence, leaving it out is more natural.

Turkish does not have articles like English a and the.

So mesaj can simply mean message in a general or indefinite sense.

In this sentence:

• mesaj atacağım = I’ll send a message / I’ll message

If you want to make the a more explicit, you can say:

• bir mesaj atacağım = I’ll send a message

If you say:

• mesajı atacağım

that usually means the message or that specific message.

Because it is a non-specific direct object.

In Turkish, a direct object often stays unmarked if it is indefinite or non-specific:

• mesaj atacağım = I’ll send a message

If the object is specific, it usually takes the accusative:

• mesajı atacağım = I’ll send the message / that message

So the lack of -ı / -i helps show that the speaker means a message, not a particular already-known message.

Yes. Turkish word order is flexible, although some orders sound more neutral than others.

The original sentence is very natural:

• Toplantı biter bitmez sana mesaj atacağım.

It puts the time expression first, then the recipient, then the main action.

You could also say:

• Sana toplantı biter bitmez mesaj atacağım.
• Toplantı biter bitmez mesaj atacağım sana.

These are possible, but the original version is probably the most neutral and standard in everyday use.

Atacağım is a clear future form: I will send.

It sounds definite and fits a specific future situation well:

• Toplantı biter bitmez sana mesaj atacağım.

If you used atarım, it could sound more like:

• a habitual action
• a general tendency
• sometimes a promise in conversation

So atacağım is the most straightforward choice when you mean I will do it later.

It is neutral to slightly informal, mainly because of mesaj atmak, which is very common in everyday Turkish.

It sounds completely natural in conversation and casual writing.

If you wanted something a bit more formal, you could say:

• Toplantı biter bitmez size mesaj göndereceğim.

That changes:

• sana → size for polite or plural you
• mesaj atacağım → mesaj göndereceğim, which sounds slightly more formal

But the original sentence is very normal and natural.