Is this scenario a bootleg ground? Is it safe? options?
The ground wires to the outlets...
...The outlets DO NOT have the ground wire hooked up at all, and no
&quot;typical&quot; bootleg with a jumper or something. Should I hook up the
ground wires in the outlets?

First off, there are ground wires TO the outlets, but they are just sitting in there? That makes no sense and if the ground wires are there, you should connect them to the ground terminals of your outlets.

...are bonded to the neutral wires in the shop's subpanel.

Secondly; is this a sub-panel or the SERVICE panel? The FIRST panel where the utility power comes in is the SERVICE panel, and you DO connect the Neutral and Ground wires together there. In a SUB-panel, you do not. If this is a sub-panel, then they should NOT be bonded (connected together), even though they are going to be at the Service panel upstream. The Service panel is where the Ground is then connected to the Grounding Electrode (ground rod) with a separate ground wire, called the Grounding Electrode Conductor (GEC). That should be the ONLY connection to ground in your building.
Thirdly, when talking about the number of &quot;wires&quot; in a service or cable, you do not count the ground conductors, it is not a &quot;current carrying conductor&quot; so is not considered a &quot;wire&quot;. So &quot;Romex 3-wire going from the breaker box to all the outlets&quot; would mean 2 hot wires and 1 neutral, not 1 hot, 1 neutral and 1 ground. I'll assume you meant 1 hot, 1 neutral and a ground, which is called 2-wire NM cable with ground. NM cable is abbreviated by the size, the the number of current carrying conductors, then w/G if there is a ground wire, so for example 14-2 w/G is 14 ga, 2 wire (H+N) with Ground. The reason it is done that way is that you used to be able to get 14-2 with no ground, in which case it was just called 14-2.
Lastly, a &quot;bootleg ground&quot; is when there is NO ground wire run out to the receptacle box, so someone bonds the ground terminal of a grounded receptacle to the neutral terminal with a little jumper. That was technically legal up until 1969 but has not been since then. But from your descriptions, that's not what you have.