Taking a taxi is probably your best option. The shuttle doesn't run quite that far out. You might find a tour bus that does a drop off there, but that would take some research. It's not a very 'touristy' place, although tourists go out there. It's also one of the few places you can get to via land travel (versus plane or boat).
Here's the deal - if you stay at Herring Cove long enough, you WILL see bears. However, given that the Disney ship doesn't stay in port as long as the others (I don't think you even get in until lunchtime), you may have to consider if it's worth spending all your time watching and waiting. If you do go... go first thing in the morning or later in the evening. And consult the tide tables. I always have the best luck when low tide falls in the evening.
Another option is to call around the flightseeing companies and see about booking a floatplane. They can get you into those obscure areas on other islands where you can see some lovely sights, including bears.
I think this is one of those occasions you have to decide if money or time is most valuable to you.