Without some project example it is difficult for me to follow what is happening. In general for me bearer tokens and property transfers have been working fine in SoapUI.
In my usage I fetch bearer token by using HTTP or REST test steps instead of using any built in mechanism in authorization tabs. With manual control you will know exactly what you are doing. When inputting bearer token to the request, you should use Header assignment by adding "Authorization" named header with value "Bearer <tokenPropertyValue>". This is in my experience most reliable way. Also remember to remove any built-in authorization options from the test steps,they may interfere "Authorization" header setting.
In your case I would suggest adding Fiddler or some other proxy in between. From there you could inspect the actual HTTP request and its header values and compare it to the working case. This way you could pinpoint any differences.
