Disclaimer: The materials provided below are informational and should not be relied upon as legal advice.
Yes, there are two was to conduct this transaction: (1) you can buy out the interest of the other LLC member, or (2) the LLC can redeem the membership interest of the other member. Although the LLC may be disregarded "for tax purposes", that would not necessarily affect the LLC's status under state law (with certain exceptions). Keep in mind that depending on how the LLC was originally set up, the LLC may need to amend its Articles of Organization and/or its LLC Operating Agreement when it changes from a two-member entity to a single member entity. Be sure to consult your own attorney to protect your legal rights.
Mr. Mashal gives a correct answer, especially on the point of "disregarded" versus "separate".
Make sure you check the tax results on a corporate redemption versus a purchase where your would end up with a basis in the shares purchased. A good tax CPA is an essential part of any business team.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
If you have a California LLC, the LLC can buy an interest from one of the members. First, you should check your operating agreement to confirm that the transfer of a 50% interest in the company does not dissolve the company. Second, check your operating agreement to see if the sale of a member interest is addressed. It is important to follow the process laid out in your operating agreement (and document it in writing), even though it only seems like a formality. If your agreement does not describe the process the sale of a member interest, you will have to agree on the terms with the selling member (whether she will sell to the company itself without a promissory note from you personally, timeframe for payment, etc.) If you have any questions or if you are ready to move forward with the purchase/sale of interest in the LLC, please consider speaking with an attorney so that your interests are protected.