Having just completed my sensational leg anatomy video course, I've come to realize that for forward bending the hips with the knees straight (a.k.a. stretching the hamstrings), it's very helpful to learn to control the long hip flexor muscles, namely the rectus femoris, sartorius, and tensor fascia latae.
I call them long hip flexors because they are long. They extend all the way from the hip bone to the tibia.
All of these hip flexors attach to the pelvis at or near the ASICs (Anterior Superior Iliac Spine) the point at the front of the hip crest. The rectus femoris attaches a little lower. This could be thought of as a major leverage point for the pelvis, just like the pubic bone, the sitting bones and even the PSIS the posterior superior iliac spine.
At the bottom end, these long hip flexor muscles attach to the outside of the tibia, the knee cap and the front of the tibia, or the inside or the tibia, just below the knee joint.
The trick in using these muscles to effectively bend or flex the hips forwards, is taking out the slack, particularly when the knees are straight.
So for example, the tensor fascia latae attaches to the IT band which passes over the vastus lateralis muscle before attaching to the top of the tibia. To take the slack out of the IT band and make it easier to use the tensor fascia latae to flex the hip, activate the vastus lateralis.
Rectus femoris passes over the vastus intermedius. And so to take the slack out of the rectus and make it easier to activate, try activating the vastus intermedius.
Now you might think that to take the slack out of the sartorius all you have to do is activate the vastus medialis. And it may help. But in my experience so far, it seems to help if I activate the inner thigh muscles, the adductors.
Note that in a standing forward bend, or even a seated forward bend, it's fairly easy to relax the quadriceps. So instead work at keeping them (and the adductors active) and see if that doesn't make it easier for you to use your hip flexors to bend your hips forwards (and so stretch your hamstrings).
For more on how to activate the muscles of the legs (including the aforementioned hip flexors and vastus muscles) check out Sensational Leg Anatomy. It includes the latest exercises that I use to make learning muscle control easier.