I suspend the bag over the BK with a pulley system. Then I either squeeze the suspended bag, or place a large colander on top of the BK, drop the bag into the colander, and then squeeze. Colander is large enough diameter so that the bag does not hang over the edge. After sufficient squeezing, the bag doesn't drip spontaneously. I use silicone gloves when squeezing for heat and "sticky" protection.
If you don't want to squeeze to the point of no dripping, then you can hoist with a pulley, slide a large diameter plastic bucket/bin under the bag, and then lower the bag into the container, so that wort doesn't get squeezed out by the sides of the container. As you mention, a typical 5 gallon bucket isn't adequate for this task (unless you have a small bag.)
There is no such thing as a universal "best brewing process." Everyone's needs, constraints and desires are different, so they need to decide for themselves what is best for them. I don't think anyone who is happy with their brewing process should change it. I also don't think people should disparage a process they don't know how to conduct well, just because they had issues for which there are known solutions. I do advocate that extract brewers wishing to upgrade to, or new brewers wishing to start out with, partial mash or all grain, start with BIAB, since it has a lower cost of entry than a traditional three vessel system. If they don't like BIAB for any reason they can move on to a more traditional AG process, and the only sunk costs are the bag (unless they continue to use it in their MLT), and maybe a pulley. Starting with three vessel and then moving to BIAB involves more sunk costs.
Brew on