Wir warten jeden Morgen an derselben Bushaltestelle.

In a normal German main clause, the finite verb usually comes in position 2.
So in Wir warten jeden Morgen an derselben Bushaltestelle:

• Wir = subject
• warten = finite verb
• jeden Morgen = time expression
• an derselben Bushaltestelle = place expression

This is one of the most basic German word-order patterns.

Sometimes yes, sometimes no.

In this sentence, warten is used without an object and simply means to wait.

If you want to say wait for someone/something, German usually uses auf + accusative:

• Wir warten auf den Bus. = We are waiting for the bus.

But in your sentence, an derselben Bushaltestelle does not mean for the same bus stop. It tells you where they are waiting:

• an derselben Bushaltestelle = at the same bus stop

So here, an is a location preposition, not something required by warten itself.

German uses certain prepositions naturally with certain places. For a bus stop, the normal choice is an:

• an der Bushaltestelle = at the bus stop

Why not the others?

• in der Bushaltestelle would sound like being inside the physical structure
• auf der Bushaltestelle would sound like being on top of the bus stop

So if you mean at the bus stop, an is the idiomatic choice.

Derselben comes from derselbe, which means the same.

It changes its form to match the noun it belongs to.
Here it describes Bushaltestelle, which is:

• feminine: die Bushaltestelle
• singular
• in the dative case after an (because this is a location, not movement)

So the correct form is:

• an derselben Bushaltestelle

This is just agreement: the word for the same has to match the gender, number, and case of the noun.

Because an is a two-way preposition. With two-way prepositions, German uses:

• accusative for movement toward a destination
• dative for location

Here, the sentence describes a location:

• They are waiting at the bus stop

There is no movement toward it in the sentence, so German uses the dative:

• an derselben Bushaltestelle

Compare:

• Wir gehen an dieselbe Bushaltestelle. = We go to the same bus stop.
  
  • movement → accusative
• Wir warten an derselben Bushaltestelle. = We wait at the same bus stop.
  
  • location → dative

Jeden Morgen means every morning.

This is an example of an accusative expression of time in German. German often uses the accusative case for phrases that answer when? or how often?

Here:

• Morgen is a noun meaning morning
• jeden is the accusative masculine form of jeder because Morgen is masculine

So:

• jeder Morgen = every morning, in dictionary form
• jeden Morgen = every morning, as a time expression in the sentence

This is very common:

• jeden Tag = every day
• jede Woche = every week
• jedes Jahr = every year

Because here Morgen is a noun, and all nouns are capitalized in German.

There is an important difference:

• Morgen = morning, the noun
• morgen = tomorrow, the adverb

So:

• jeden Morgen = every morning
• morgen = tomorrow

Capitalization changes the meaning.

Yes. German very often combines nouns into compound nouns.

Bushaltestelle is made of:

• Bus = bus
• Haltestelle = stop

Together:

• Bushaltestelle = bus stop

The final part of a compound is the main noun, so the gender comes from Haltestelle, which is feminine:

• die Haltestelle
• die Bushaltestelle

That is why you get:

• an derselben Bushaltestelle

Yes. In everyday German, an der gleichen Bushaltestelle is often more common than an derselben Bushaltestelle.

Both can mean at the same bus stop.

A rough distinction sometimes taught is:

• dieselbe = the very same one
• die gleiche = one that is identical/the same kind

But in real everyday usage, many speakers use dieselbe and gleiche quite loosely, and die gleiche is extremely common where English would just say the same.

So your sentence could also be:

• Wir warten jeden Morgen an der gleichen Bushaltestelle.

Both are correct.

That is a very common German word-order pattern: time before place.

So German often prefers:

• Wir warten jeden Morgen an derselben Bushaltestelle.

rather than:

• Wir warten an derselben Bushaltestelle jeden Morgen.

The second version is possible in some contexts, but the first sounds more natural as a neutral statement.

A useful beginner rule is:

• subject – verb – time – place

So this sentence follows a very standard pattern.

Yes:

• Jeden Morgen warten wir an derselben Bushaltestelle.

That is perfectly correct.

German lets you move one element to the front for emphasis or style, but the finite verb still stays in second position. So if Jeden Morgen comes first, then the verb warten must come next, before wir.

This is a very common feature of German word order.