This year my husband and I went for Hajj. When the people in our group wanted to go to Muzdalifah, they asked everyone: Who wants to stay overnight in Muzdalifah and who does not? When they found out that there were some people who wanted to stay overnight in Muzdalifah, they said to us: Wait until the bus comes. The bus came at 10 PM and we got on, but the bus was so slow that we only reached Muzdalifah at 7 AM. Do I have to offer a sacrifice, because I was not able to enter Muzdalifah and stay there overnight or pray there?

Praise
be to Allah.

Firstly: 

Staying overnight in Muzdalifah is
obligatory according to the majority of scholars; some of them are of the
view that it is a pillar or essential part of Hajj. 

There was a difference of opinion as to
how long one must stay there. The view of the Shaafa‘is and Hanbalis is that
staying in Muzdalifah is obligatory, even if it is only for a moment, so
long as that occurs in the second half of the night, after standing in
‘Arafah, and it is not essential to stay there; rather it is sufficient to
simply pass through it. 

So if you had entered within the
boundaries of Muzdalifah, even for a moment, between halfway through the
night and dawn, then you have done what is required. 

But if you were not able to enter
Muzdalifah because the roads were so crowded, then you do not have to do
anything (to compensate for that), because obligatory duties are waived when
one is unable to do them. Allah, may He be exalted, says (interpretation of
the meaning): “On no soul does Allah place a burden greater than it can
bear” [al-Baqarah 2:286]

Shaykh Ibn Baaz (may Allah have mercy on
him) was asked: We were not able to stay overnight in Muzdalifah because we
could not find any space except on the road, and they do not allow anyone to
stop in the road, so we left and went to Mina. Do we have to do anything (to
compensate for that)? 

He replied:

If there was no space in Muzdalifah or the
troops did not let him stop, then he does not have to do anything (to
compensate for that), because Allah, may He be glorified, says
(interpretation of the meaning): “So keep your duty to Allah and fear Him
as much as you can” [at-Taghaabun 64:16]
. But if that was due to
carelessness on his part, then he has to offer a sacrifice and also repent.

End quote from Fataawa Ibn Baaz
(17/287) 

See also the answer to question no.
14632 

Secondly: 

You made a serious mistake by delaying the
prayer until the time for it was over, because that is haraam and is in fact
a major sin. Allah, may He be exalted, says (interpretation of the meaning):

“Verily, the prayer is enjoined on the
believers at fixed hours”

[an-Nisa’ 4:103]

“Then, there has succeeded them a
posterity who have given up As-Salat (the prayers) (i.e. made their Salat
(prayers) to be lost, either by not offering them or by not offering them
perfectly or by not offering them in their proper fixed times, etc.) and
have followed lusts. So they will be thrown in Hell”

[Maryam 19:59]

The Sunnah is to delay Maghrib and put it
together with ‘Isha’ in Muzdalifah, but if a person is afraid that the time
for ‘Isha’ will end before he reaches Muzdalifah, then he has to pray on the
road, according to his situation. If he is walking, he should stop and pray,
standing, bowing and prostrating; if he is riding (in a vehicle) and cannot
get off, he should pray on board that vehicle, because Allah, may He be
exalted, says (interpretation of the meaning): “So keep your duty to
Allah and fear Him as much as you can” [at-Taghaabun 64:16]

If a person remains in ‘Arafah until
approximately 10 PM, and is aware that the roads are crowded, it is better
for him for him to pray Maghrib and ‘Isha’ in ‘Arafah, especially if he has
women with him, for whom it is difficult to get off and pray in the road. 

The point is that one should not neglect
what is obligatory for the sake of something that is Sunnah. 

What you have to do is repent to Allah,
may He be exalted, for having delayed the prayer, but you do not have to do
anything else. 

And Allah knows best.