The spell is still affecting the druid, and wild-shaping does not end effects on the wild-shaper, therefore the druid is still under the effects of the enlarge spell while wild-shaped.

At this point you might conclude that the question is settled: they would be an extra-large bear, because the spell is still working that that's what enlarge does. But that's not quite right.

Let us look at precisely what the enlarge spell's effect is, not what we might be tempted to mentally simplify it as (with all emphasis mine):

You cause a creature or an object you can see within range to grow larger or smaller for the duration.

Okay, so it doesn't make it 2× in every dimension as a static fact, it makes it grow at the beginning of the spell. That would mean it would not make any further changes afterwards, only sustain the initial change.

Well, maybe I'm reading too much into "to grow". Let's see what else it says it does:

The target's size doubles in all dimensions, and its weight is multiplied by eight. This growth increases its size by one category — from Medium to Large, for example. If there isn't enough room for the target to double its size, the creature or object attains the maximum possible size in the space available. Until the spell ends, the target also has advantage on Strength checks and Strength saving throws. The target's weapons also grow to match its new size. While these weapons are enlarged, the target's attacks with them deal 1d4 extra damage.

So it does look like it's a one-time growth, based on the verbs and nouns used. In particular, if enlarge is used on a target inside a smaller space than the maximum possible size, and then the target moves out of that space, they don't grow further once there is more room — the growth at the beginning of the spell is all you get, nothing more later.

So, the conclusion there is that the druid can shapechange into a form, and the enlarge effect is not applied to the new form. If they change into a sparrow or a bear, they get the normal statistics of a normal sparrow or normal bear.

That means that a druid that wants to dodge an inconvenient enlarge or reduce can easily do so by wild-shaping, but a druid that wants to benefit from enlarge or reduce in their wild-shaped form will have to somehow arrange for the spell to be cast after they wild-shape, so that it will grow their new form instead of just their previous form.

Yes, the jump is the distance from the ground to the bottom of your feet

When you make a high jump, you leap into the air a number of feet equal to 3 + your Strength modifier [...] Either way, each foot you clear on the jump costs a foot of movement.

Intuitively, a vertical jumping distance makes the most sense as the distance between your shoes and the ground but really your entire body is moving the same distance upwards. The rules' language talks of the distance you "clear" and "leaping into the air" both of which evokes the imagery of the gap between ground and shoes. More direct evidence can be found in the following passage:

You can extend your arms half your height above yourself during the jump. Thus, you can reach above you a distance equal to the height of the jump plus 1 1/2 times your height.

So it is clear from the rules that when you jump, the distance is measured from the ground to your feet and that means that the rest of your body moved vertically that same distance.

If the PC can jump X feet, their feet reach X feet

If a 6' tall character jumps up 8' it means that their feet are 8' above the ground and their head is 6' + 8' = 14' above the ground. If they raise their arms the tips of their fingers would be 1.5 * 6' + 8' = 17' feet above the ground.

In this case, if a character jumps up at a 8' wall with a jump of 8', then the assumption is that they land on their feet on top of the wall.

The way the jump looks narratively is not defined

How all this jumping and leaping looks is completely situational and also not at all defined in the rules. In cases like these, the DM must fill in the blanks.