Salam alaikum.

I seen many times when shia accused sahabe Asma bintu Abu Bakr, that she commited mutah.

As a proof they are giving narration from “Musnad” of Taylase.

حدثنا يونس قال حدثنا أبو داود قال حدثنا شعبة عن مسلم القرشي قال دخلنا على أسماء بنت أبى بكر فسألناها عن متعة النساء فقالت فعلناها على عهد رسول الله صلى الله عليه وسلم

Narrated Yunos narrated Abu Dawood narrated Sho’ba from Muslim al-Qurashi he said : we visited Asma bint Abi Bakr and we asked her about MUTA OF WOMEN so she said : WE did it during the time of rasool Allah

First of all even from this text, it’s not clear that Asma (r.a) did mutah herself. For example if someone would ask: DOES MOSLEMS MAKING SACRIFICE? I would reply: YES WE DO THAT. But I personally never done it with my own hands.
So answer of Asma: We did it during the lifetime of prophet (sallalahu alaihi wa ala alihi wa sallam) doesn’t mean that she did it personally.

Also we should notice that there is other version of this hadith.

Tabarani in “Kabir”:

277 – حدثنا عبد الله بن أحمد بن حنبل و محمد بن صالح بن الوليد النرسي قالا : ثنا أبو حفص عمرو بن علي قال : ثنا أبو داود ثنا شعبة عن مسلم القري قال :
: دخلنا على أسماء بنت أبي بكر فسألناها عن المتعة فقالت : فعلناها على عهد رسول الله صلى الله عليه و سلم

Muslim al-Qurashi said : we visited Asma bint Abi Bakr and we asked her about MUTA so she said : WE did it during the time of rasool Allah (sallalahu alaihi wa ala alihi wa salam).

As you can see here, the talk wasn’t about mutah of women, but mutah in general, and that could mean mutah al-haj. Allah knows better.
And there is another great proof, that Moslem was asking about haj at-tamattu in sahih of imam Moslem:

Sahih Moslem.
Chapter 27: CONCERNING TAMATTU’ IN HAJJ

Book 007, Number 2854:
Muslim al-Qurri reported: I asked Ibn Abbas (Allah be pleased with them) about Tamattu’ in Hajj and he permitted it, whereas Ibn Zubair had forbidden it. He (Ibn ‘Abbas) said: This is the mother of Ibn Zubair who states that Allah’s Messenger (may peace be upon him) had permitted it, so you better go to her and ask her about it. He (Muslim al-Qurri said): So we went to her and she was a bulky blind lady and she said: Verily Allah’s Messenger (may peace be upon him) permitted it.
Book 007, Number 2855:
This hadith has been narrated on the authority of Shu’ba with the same chain of transmitters, but with a slight variation of words.

To benefit more on this topic [ Taken from research done by sh. Faisal al-Jassim]:

All the routes of this hadeeth is reported from the way of Shu’ba from Muslim al-Qarri from Asmaa.
The following are the narrators who reported this Hadeeth from Shu’ba and they disputed over its text:

a. Yunus bin Habeeb and Mahmoud bin Ghilaan from Abu Dawd from Shu’ba with the text {Mu’ta of women}. [Musnad al-Tayalsi and Sunan Nasaie]
b. Amro bin Ali and Ibn Abdullah al-Saffar from Abu dawd from Shu’ba without the word “women”. So its text is: {We asked her about the Mu’taa}. [al-Mu’jam al-kabeer by Tabarani]
c. Abdurrhman bin Mahdi from Shu’ba without the word “women so the text of this route is {We asked her about the Mu’taa} [ Sahih Muslim and others]
d. Ghandar from Shu’aba who said: Muslim said: I do not know whether it was the Mu’taa of Hajj or the Mu’taa of women” [Sahih Muslim]
e. Rawh bin Ubadah from Shu’ba: {Mut’aa of Hajj} and in this report he mentioned the full story: he said: I asked Ibn Abbas about the Mu’taa of hajj so he allowed it while Ibn al-Zubair did not allow it. So Ibn abbas said: go to his mother as she narrate that the Prophet permits it as well and ask her about this matter. So we eneterd upon her and she was blind huge woman and said: The Prophet permitted it” [ Sahih Muslim]

the following can be noted:
The Mu’taa of women was only reported from Abu dawud. However, who reported it from his way disputed over it; one said it “Mut’aa of women” while others reporting from him that he said: “The Muta’aa” without the word women.

The rest of routes are clearly show that what is preserved that it is about Mu’taa of Hajj.