I can't level my bed any more
The bar where the level is attached is the support cross-bar for the X-axis travel. 

It's important this bar be level, but it's even more important the bar be true to the rest of the machine. We call this "leveling" the printer, but really the more accurate term is "tramming". If the bar is level, but the machine sits on an unlevel surface, things are out of sync. This may be the case here.


  I did this by unplugging the wire to one motor and modified the z-position so that the other connected side would go up. (Is this the proper way of adjusting the horizontal bar?)


No. The first image in your question shows two threaded vertical rods: one on the left that is exposed, and one on the right that is more hidden (only a small portion is visible between the two "A" labels). These rods control travel in the vertical "z" direction. Each rod has an inline coupler connecting it to the Z-stepper motors. The coupler for the right side is visible just below the square label "A". You adjust the level of the X cross-bar by turning the couplers while the printer is turned off or the motors are otherwise disengaged. This allows you to make finer adjustments for the bar, often without needing to re-home the Z axis.

You can also use this method to correct your immediate problem.

I own a Select Plus, which uses similar construction to your Select V2. When I first got the printer one of my couplers was not adequately secured to the rod. This made for all kinds of difficulty leveling the bed at first, including at one point an issue similar to what you are experiencing.

Re-leveling the X cross-bar is easiest if you are first certain the printer itself is on a level surface. If this is the case, you should be able to use the level in the images to check the cross-bar in the same way you did previously, making adjustments via couplers. But check that surface first. If the surface is not level, you need to adjust the X cross-bar to be parallel to something in the machine other than the bed. While we want the bed to match the rest of the machine, the very fact you can adjust this means it's not guaranteed at any point in time, and so you should use something more structural to compare against. 

In this case, you can place the same level across the two steel Y-axis travel bars below the bed, and check where the bubble sits. Then make sure the bubble ends up in exactly the same position for the X cross-bar, regardless of whether or not that's level to the ground. The greater precision you can get here, the better things will be.



I'm gonna add some notes about leveling the beds on these specific printer models.

There are three basic types of leveling:


Manual. You do everything yourself.
Assisted. You still do most things yourself, but the machine will help by moving the head quickly to certain positions for you to check. This is what many machines refer to as "automatic", even though it really isn't.
Automatic. This is where the machine does everything, using lasers to map the bed or some other contact sensor to detect when the head approaches the bed and make it's own adjustments. Often this only uses software to compensate for the bed, and so you still want to get the bed as level as possible first without this option.


The Select V2 and Select Plus only do #2: assisted.

When I was starting out, my research indicated you should generally level your print beds "hot", because heating a print bed will expand it and potentially change the results. This makes sense to me. 

However, the instructions included with my Select Plus said nothing about heating the bed, and if followed precisely meant I leveled a cold bed. Additionally, the so-called "automatic" (really: "assisted") leveling tool in the firmware also does not keep the bed heated, meaning if you want to level it hot you must do it entirely manually. 

This caused me great difficulty when first starting out getting a good level, because I was trying to do it manually on a hot bed. I finally gave up on that, and started using the assisted tool on a cold bed. To my surprise and relief &mdash; and counter to what I've read elsewhere &mdash; I've had much better results when doing it cold this way. But this may be some peculiar to these printers, perhaps involving the special mat it uses on the surface of the bed.

I'm also considering this upgrade (Update: I recently installed it, but it's too soon to know if it's helping), to help improve things even further, since there is some curvature in my plate:


  https://www.amazon.com/dp/B07B251KBS/


Finally, there's an interesting seesaw effect when working on a square print bed with four adjustment knobs. I have a post about it here:


  Leveling a square 3d printer bed with four mounting posts