FOUND IT! It is not a pretty one, but is works.
In older versions of vmware workstation an player there was a tool for configuring network adapters. It is called vmnetcfg.exe. In the newest version of vmware workstation it is still in the install package, but not installed anymore. To get it to work in my vmware player id did this:
Get the Program
I downloaded the latest version of VMware Workstation (400+MB). When it completed I opened up CMD and extracted the installer:
> cd \path\to\installer\
> vmware-workstation-versionyaddayadda.exe \e extractedfolder
Then I went to the extracted folder and opened core.cab with winrar. Somewhere in there hides a vmnetcfg.exe. I extracted it and copied it to my VMware Player install folder.
Running te program
I started the program. I had a VMnet0, VMnet1 and VMnet8 listed. I selected VMnet0 in the list, then clicked bridged and selected my wireless network adapter instead of automatic.
Then I clicked "Add Network..." and called it VMnet2. I selected VMnet2 in the list, then clicked bridged and selected my wired network card instead of automatic.
Adding the card to the VM
First I added the second virtual network adapter in the VMware player's machine settings. The first one I kept on bridged, and configured the wireless adapter as the preferred bridge adapter (my wired adapter is not clickable anymore).
I needed to add the card to the VM by hand. This meant I had to open the VMX file in Notepad or in my case another preferred editor.
In the VMX file I added two lines (if they already exist, replace them.)
ethernet1.connectionType = "custom"
ethernet1.vnet = "vmnet2"
I saved the file and started vmware player. In my network settings I see this now:
Network Adapter: Bridged (Automatic)
Network Adapter: Custom (vmnet2)
I started the Virtual machine, and it worked!
Best Answer
Last I tried that at work, it did not work.
Today I tried that again at home. First I connected with only the Bridge Service checked. The guest could not connect to the internet. Then I checked IP4. The guest could connect to the internet. Now I unchecked IP4 (leaving only the Bridge Service), and curiously, the guest could still connect to the internet. Even after guest reboot, the guest could connect to the internet.