Please remember that "snapshotting dots" is not in and of itself anything 'special'. There is nothing that "snapshotting" dots does that is different from any other attack during RS and other CDs.

With that said, simply treat dots as an upfront nuke when determining the value of cooldowns.

So now bio is simply a "nuke" with 240 potency. With RS, it becomes 298 potency. Simple as that. You'll note it gains 48 potency - this is slightly more than 1 tick's worth, so we'll take that into consideration in just a second.

The big deal with Bio first is that you delay your first fester, meaning its harder to fit fester into the rotation. So if we consider this, with 0 spell speed, it will take you

[Bio II] > [Miasma] > [Bio|Swiftcast|Fester] is the first rotation, so it takes you roughly 6.5 seconds to get a fester out. This gives you 16.5 seconds for the second fester, or if you think about it, 3.5 seconds of leeway.

If you bio first, it turns into

[Bio] > [Bio II] > [Miasma] > [Ruin II|Swiftcast|Fester] so it will take you ~9 seconds for first fester.

This gives you only 1 second of leeway. Now, in an ideal scenario, this will work, but...you're playing with fire here. This is my primary motivator in not Bio first. Now, if you remember our potency discussion, you gain 48 potency for Bio during RS. Since fester is 300 potency, you gain 60 potency for doing it during RS. Needless to say, if you miss out on the second fester, you will lose more dps, and Bio is not worth it.

We also consider whether or not it is worthwhile to clip Bio prior to end of RS, for the Bio II > Miasma > Bio opener. In this opener, Bio comes out roughly around 5 seconds, with lets say .5 second delay from RS animation and Bio delay. So with 5.5 seconds, we have ~14.5 seconds before end of RS, meaning we can fit at most 5 more GCDs (6 total including first Bio GCD). This is almost exactly 3 seconds left on the tick, which means we lose on average 1 tick. Since 1 lost tick is 40 pot and RS is 48 potency, this is tentatively good. However, this comes at the cost of losing a RS II instead, which gains 16 potency, so is a loss overall. Thus, do not preemptively refresh your Bio if you do the "standard" opener.

Back to the opener you proposed, again the sticking point is whether or not you can put in that second fester. Another note to point out is, if you did not precast shadowflare, this delays your sflare for another GCD. So, again, not optimal. Loss of an sflare tick + RuinII bonus will cost you any benefit.