My weed eater will not start

It sounds like the bulb is not sealed properly. That may also explain why it shut off after 20 secs. (sucking air and not getting enough gas). Fuel line or carb may be cracked or clogged. Or you may have accidentally reversed the fuel lines. Since it worked fine before you removed it, the problem most likely lies with the bulb, its gasket, its fuel line connections or the one-way valve beneath the bulb.
Good luck

Check the plastic lines going to and coming from it. As they age they can crack.

Shauna, Primer bulb replacement. Check the attached links,instruction and guides, Good luck
"I hope this helped you out, if so let me know by pressing the helpful button. Check out some of my other posts if you need more tips and info."
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If it's the one that comes 'out' of the primer bulb it is the return line that goes in the fuel tank.

Sounds like bulb not seated well...check to make sure it has all seals in place. Some pop in, some seal with a rubber seal.

FIXED- No start Weed Eater with the symptom of the primer bulb collapsed, not filling nor returning to pop out after pressed.

Worked in model WT-3100 with Walbro carburetor WT-583 and has to work in many others. It happened after winter hibernation, even when left with no fuel to prevent formation of fuel deposits.

FIRST, mark/scribe the carburetor fuel outlet that has the hose towards the primer purge bulb as 'OUT' and the fuel inlet coming from the fuel tank 'IN'
The problem was a fine mesh metal screen strainer blocked by contaminants, inserted at place shown as number '3' in figure 7 at
----> www.drystacked.com/Walbro%20Carburetor%20Theory%2027Jun2010.pdf
That fine mesh was removed by prying its edges around with a sewing needle held by pliers.
It you cannot see light trough it holding it against a lamp, is blocked even if looks clean.
Removed, discarded, reassembled and started. Later ordered the part or kit but was able to use the machine immediately.

Writing this as am tired of seeing responses like 'may be this' or 'try that' or 'perhaps the other' by guessers.

change the fuel lines over on the carby
you are trying to feed fuel through the primer line when the engine is running and that is why it is cutting out

If you see gas in the primer bulb it is pulling in gas to the bulb. If not check for cracks in the bulb assembly and check to see if the fuel lines are not off their fittings and not cracked.

You have a hairline leak in one of your hoses or a small gasket under primer bulb.

somewhere on it is a primer button pump it a few times and choke the blower it should start