Are those Bedouin who became Muslim and some of them behaved badly towards the Prophet (blessings and peace of Allah be upon him) regarded as being among the Sahaabah?

The Sahaabi is the one who saw the Prophet (blessings and peace of Allah be upon him) and was a believer in him, and died in that state of belief. 

Imam al-Bukhaari (may Allah have mercy on him) said in his Saheeh (3/1333): Whoever  among the Muslims accompanied the Prophet (blessings and peace of Allah be upon him) or saw him is one of his companions. End quote. 

So everyone who meets this description is one of the Sahaabah, and it is not permissible to impugn him or criticise him, because of the general meaning of the words of the Messenger of Allah (blessings and peace of Allah be upon him) according to the report narrated by al-Bukhaari (3673) and Muslim (2451) from Abu Hurayrah (may Allah be pleased with him): “Do not revile my companions, do not revile my companions. By the One in Whose hand is my soul, if one of you were to spend the equivalent of Uhud in gold, it would not amount to a mudd of one of them, or half of that.” 

Secondly: 

The Sahaabah (may Allah be pleased with them) vary in virtue and status. Allah, may He be exalted, says (interpretation of the meaning):

“Not equal among you are those who spent and fought before the conquering (of Makkah) (with those among you who did so later). Such are higher in degree than those who spent and fought afterwards. But to all, Allah has promised the best (reward)”

[al-Hadeed 57:10]

“And the first to embrace Islam of the Muhajiroon (those who migrated from Makkah to Al-Madinah) and the Ansaar (the citizens of Al-Madinah who helped and gave aid to the Muhajiroon) and also those who followed them exactly (in Faith). Allah is well-pleased with them as they are well-pleased with Him. He has prepared for them Gardens under which rivers flow (Paradise), to dwell therein forever. That is the supreme success”

[at-Tawbah 9:100].

And He said concerning those who became Muslim later on and did not attain the same status as the earlier Muslims:

“And He has sent him (Prophet Muhammad (blessings and peace of Allah be upon him)) also to others among them (Muslims) who have not yet joined them (but they will come). And He (Allah) is the All-Mighty, the All-Wise.

That is the Grace of Allah, which He bestows on whom He wills”

[al-Jumu‘ah 65:3-4]. 

Thirdly: 

Undoubtedly none of the senior Sahaabah and the earlier ones among the Muhaajireen and Ansaar – foremost among whom were the ten who were given the glad tidings of Paradise and those who were present at Bay‘at ar-Radwaan – ever behaved badly towards the Messenger (blessings and peace of Allah be upon him). Rather all the cases of behaviour that was not appropriate to the status of the Prophet (blessings and peace of Allah be upon him) – which were few in number – only happened in the case of some people who were new in Islam and in whose hearts faith had not yet taken firm root. Many of them were people of the desert (Bedouins) and it is well-known that the desert people were characteristically rough and harsh in their dealings with others. Imam Ahmad (18619) narrated with an isnaad in which there is some weakness that al-Bara’ said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever lives in the desert will become rough.” 

But this conduct on their part does not mean that we should criticise or impugn them, because they became good Muslims after that and accompanied the Prophet (blessings and peace of Allah be upon him) in the best manner, and they strove in jihad with him. Hence Allah, may He be exalted, says (interpretation of the meaning):

“And of the bedouins there are some who believe in Allah and the Last Day, and look upon what they spend in Allah’s Cause as approaches to Allah, and a cause of receiving the Messengers invocations. Indeed these (spendings in Allahs Cause) are an approach for them. Allah will admit them to His Mercy. Certainly Allah is Oft-Forgiving, Most Merciful”

[at-Tawbah 9:99]. 

Shaykh Ibn Sa‘di said: This verse indicates that the Bedouin were like the townspeople: some of them were good and some of them were otherwise. Hence Allah did not criticise them simply for being Bedouin and people of the desert; rather He criticised them for neglecting the commands of Allah, because they were likely to do that.

End quote from Tayseer al-Kareem ar-Rahmaan (394). 

Many blameworthy actions were committed by either the hypocrites or by those who were new in the faith, in whose hearts faith had not yet become fully established. 

Whatever the case, what you mention about hating them or reviling them and the like is wrong, because some of the Bedouin believed in Allah and His Messenger. Moreover there is no need for such attitudes at all, and it creates mischief or exposes one to mischief, without serving any shar‘i interest worth mentioning. It does not follow any command or instruction, and it does not help one to attain any virtue. 

For more information, please see the answers to questions no. 106419, 180550 and 131936 

And Allah knows best.