I've got my '71 Rocket 3 running pretty nice now. I've installed a Tri-Spark ignition system & coils, and it fires right up after tickling all 3 carbs but dies after a few seconds, starved for fuel. Once it warms up there's no problem starting it.
...And that's the reason carbs have chokes (or some form of enrichment system).
Is this a problem on these bikes? I have a '70 Bonneville that fires right up and keeps running no problem. (My first triple)
No, the problem is there are no 'chokes' fitted. An engine that starts and runs well from cold without enrichment is running too rich
so it's your Bonneville that has the "problem".
However, you can keep the engine running by momentarily pressing the ticklers until the engine has warmed up.