Yes, a traveler with a B-1 visa who is eligible for the VWP can use the VWP for visits that do not have a business purpose. However, your visa is a B-1/B-2 visa, so you shouldn't use the VWP at all. Your visa permits both personal visits and business visits. When you enter the US, you have to tell the officer the purpose of your trip, and the officer would then admit you either in B-1 or B-2 status, as appropriate.
In theory, the VWP is only for people who don't have an appropriate visa, because if they do have one, there is no need to waive the visa requirement. Sometimes, though, people who have a visa are admitted erroneously on the VWP.
In any event, you would realize no benefit by visiting under the VWP. Suppose you spend ten weeks in the US visiting your partner, and then you leave for a month, and then you return and seek entry in B-1 status for some business meetings. The decision to admit you will be the same regardless of whether previous visit was with a B visa or the VWP. On the other hand, there are some potential disadvantages to using the VWP, most notably that you cannot extend your stay if your circumstances change.
The other answer shows some misunderstanding of the time limits associated with the B visa. When you are admitted on a B visa, you will be admitted for at least six months (not 180 days) unless there is some unusual circumstance. You can actually be admitted for up to one year. Furthermore, you can apply to extend your stay in six-month increments. As the other answer correctly notes, this can expose you to income tax liability, and you also have to be able to explain how you can manage to spend so much time in the United States without doing any work, but it is theoretically possible.
Furthermore, if you visit for personal reasons and then suddenly have a need to attend a business meeting, you can apply to change your status from B-2 to B-1. In practice, that will probably take too long to be useful, and you may be better off leaving the country and returning. The application to change or extend nonimmigrant status is also somewhat expensive, carrying as it does a fee of $370.
Under the VWP, by contrast, you cannot extend your stay, nor can you change to another status.
The six-month minimum period of initial admission is specified at 8 CFR 214.2:
(b) Visitors -
(1) General. Any B-1 visitor for business or B-2 visitor for pleasure may be admitted for not more than one year and may be granted extensions of temporary stay in increments of not more than six months each...
(2) Minimum six month admissions. Any B-2 visitor who is found otherwise admissible and is issued a Form I-94 (see § 1.4), will be admitted for a minimum period of six months, regardless of whether less time is requested, provided, that any required passport is valid as specified in section 212(a)(26) of the Act. Exceptions to the minimum six month admission may be made only in individual cases upon the specific approval of the district director for good cause.
Shorter periods of admission are generally reserved for cases in which someone has been in the US recently, or in which the visitor's passport expires before the end of the normal period of admission (or in less than six months after the end of that period, depending on the country issuing the passport). The situation for the VWP is not quite so obvious from looking at the statute and the regulations, but you can see that it is essentially similar by looking at the bottom of page 116 of the CBP Inspector's Field Manual:
All VWP admissions are for 90 days unless the applicant’s passport is valid for a lesser period...
(The case of someone returning to the US before the expiration of their prior period of admission is covered elsewhere.)
So, to summarize for your case:
Since you have a B-1/B-2 visa, when you visit your partner and plan no business activities during the visit, you should request admission in B-2 status. But entering with the visa to visit your partner will not have any more negative effect on your future business visits than would entering on the VWP.