How can I Bevel this sphere correctly?

Absolutely nothing wrong with @David Wilson's answer.. this is a more Subdiv. approach..

Under 2 levels of subdivision..

1. On a 36 sided UV sphere, pole vertices deleted, select every sixth longitude (select 2 edges at the right spacing, CtrlShiftNupad + to progressively select the rest, then Header > Select menu > Loops > Edge loops)
2. CtrlB Bevel those longitudes with 2 segments
3. AltE Extrude those bevels along their normals to form the external struts. And under O proportional editing, smooth,SShiftZ scale the longitudes midway between the struts inwards to make the dimples.
4. CtrlR cut a ring around the poles, including the ends of the already extruded struts, and extrude that, to male a 'fitted' rim.
5. Select the longitudes at the bottom of the dimples, and CtrlNumpad + in vertex mode expand the selection to the vertices between the struts. From the right-click menu, > Smooth those vertices. This will put a bit of 'tension' between the struts, and has a nice side-effect of creasing the fabric a little round the rim.
6. If you want the inner struts to push those segments out again, bevel those with one segment, this time, for a softer curve, and SShiftZ scale out in XY.

You may not want the details here.. but it's always nice to try things a few different ways.

Update to the answer below

I see actually that it has 12 sides, so create 36 segments not 24, and change your edge selections accordingly and the 'Auto Smooth' value

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I'm pretty new to Blender and I had a quick go at this using a feature I learned about today "Auto Smooth".

Looking at the lampshade, it looks like it has 6 sides, so I created the UV sphere and before doing anything else at all, set the number of segments to 24. Please ignore the origin point as it's not important.

Then, I chose every 4th vertical edge using Alt+Left-Click for the first and Shift+Alt+Left-Click for each subsequent one.

Then using S and then Shift+Z so that only the x and y axes are scaled, I scaled those edges inwards toward the centre of the sphere.

Then I deselected them and selected each edge that was next to the edges I had just scaled:

And scaled them again using S and Shift+Z

OK. Getting close now. Go back to Object Mode and it still doesn't look quite right.

If I Right-Click on the sphere, and choose 'Shade-Smooth', that's no good because it smooths ALL the edges and you want to keep 6 of them sharp still. Leave the sphere smoothed at this point even though it looks wrong

I found out about Auto-Smooth and this might be what you're looking for.

Click on the Object Data tab - I'm using 2.90a, but if you're using 2.83, I think its in the same place...

Then click on the 'Normals' section and check the box next to 'Auto-Smooth' and I found that setting the angle value to 15.3 seems to produce what I suspect you want.