We did this twice on our last trip (from BC) - once to Boma, once to Jiko. Let me say, transportation really stunk. A few issues to consider - no hotel to hotel buses, and AKL closes early enough that return transportation that way may be a factor.
On our first trip we took the bus to DTD, then from there to AKL. I would say it was at least 30-45 minutes, although I can't remember exactly. We were so bus sick afterwards. I am not sure why they told us to go through DTD, but I think through AKL would been faster. On the way back, we went through MGM (AKL to MGM) and then walked to BC. This is a pretty easy walk along a nice path. It was very pleasant and nice not to have to transfer buses.
The second trip (to Jiko) was over our anniversary and we decided to take a cab. It was about $15 each way. Well worth it as it was so much more relaxing.
If you can manage it, your easiest bet (at least going there) is to leave right from the park and then you only need one bus. JJ