There's a bit to unpack here...
Before getting to your question, I'd suggest checking your visa to see exactly what type it is. It's rare for the US to issue a "B1" visa to a national that is eligible for the Visa Waiver Program - more normally they would issue a "B1/B2" visa which can be used equally for business or tourism. This doesn't fundamentally change the answer below, but it's worth understanding.
Now, lets talk about "duration of status". ie, how long you can stay in the us on a single trip. If you enter the US under the Visa Waiver Program (ie, "using" your ESTA) you will be granted a duration of status UP TO 90 days. Normally this will be 90 days, but it can be less - we'll get to that shortly. If you enter using a Visa (B1 or B1/B2), then you will be granted a duration of status of UP TO 180 days. Again, normally 180, but can be less. This is where your type of visa becomes important, as if you are entering in B2 status (using the visa) you'll likely get a longer potential stay than entering under the VWP program (normally deemed 'WB2' status)
The number above control how long you can stay on a single trip. Once you leave the us (with a few exceptions such as a short trip to Canada/Mexico), your status for that trip is over, and the next time you enter you'll be given a new duration of status, for another "up to" 90/180 days.
OK, so lets talk about "up to". Border officials will normally give you the full 90 (VWP) or 180 (Visa) days - unless they have a reason not to. One of the reason they can give you less is if they believe that you are spending too much time in the US - in effect if you are attempting to "live" in the US.
There's no formal rule for what is considered "too much time", but the general (documented) rule of thumb is that you should be spending more time outside of the US than inside the US. ie, if you come to the US for ~3 months and then leave, then you would generally be expected to spend ~3 months out of the US before you were admitted again - especially if you were entering under the VWP. If you were to return after only (say) 1 month outside of the US, it's very possible that you would either be denied entry, or possibly given entry, but only for a period much shorter than 90 days.
If you were entering on a visa (which generally allows a ~6 months stay) they would potentially be a little more lenient in the situation described above, but it's still very possible they would give a shorter period of stay for the second trip - otherwise you could be spending up to 9 out of a 10 month period in the US which is very much the definition of "living" in the US.
This isn't a hard-and-fast rule, and will depend on the exact circumstances. The fact you are first visiting for leisure and then subsequently for business MAY mean they are a little less concerned. The fact you have a partner in the US MAY mean they are MORE concerned that you are planning to live in the US. It will all depend on the exact circumstances, the moods the border staff are in the at the time, and even things like your body language and how truthful you are with them (eg, if you try and hide the fact you have a partner in the US and they find out, the odds of you being denied entry increase significantly)
So putting that all together, a personal trip won't necessarily "use up" your 6 months (actually 180 days) as such, but depending on the length of the personal trip and the time between that trip and the business trip, it certainly could result in you being granted a duration of status on your second trip of less than 180 days.
There is also a 2nd issue you need to consider, which is the IRS's "Substantial Presence Test" which controls whether you are considered a United States resident for tax purposes. If you spend more than 183 days in the US in any calendar year, you are deemed a resident for tax purposes and will need to (at least) lodge a tax return. If you spend less than 183 days, but spend time in the preceding 2 years you may also fall into this category.