Rather than being a function of its etymology, predominantly sounds to this linguist like an analogical neologism based on the following relationships:
dominate : dominant : dominantly : -- where all three refer to POWER --
: predominate : predominant : predominantly -- where all three refer to NUMBER.
Of course, there is power in numbers, but not always. For example, Old English was the predominant language of England after the Norman Conquest, but because French became the dominant language, Old English was largely relexified to become Middle English, which can thus be seen as at least in part a French creole.
No single term would cover both viruses and bacteria because there are other biological entities that are similar enough to each, such as prions or protozoa, that would need to be covered by a word that included viruses and bacteria.
The context in which you want to use this term would be useful. For non-technical audiences, you already said that microbe would work because you believed it included viruses. (And I think most non-technical readers would believe the same thing.) Germ might be a better word than you give it credit, for non-technical audiences at least.
Germ is a deceptively simple word that came to us from Latin germen, meaning a sprout, bud, or offshoot. In all of its meanings, the term germ retains the idea of developing into something more mature.
From MedicineNet. Germ as used in the phrase, germ theory of disease, means a small thing that develops into a mature disease.
For technical audiences, I think you accidentally made the best phrase in your question and comments. Something such as sub-multicellular biological entities with basic reproductive capabilities is precise, clear, and unambiguous. A technical reader will understand that this at least includes viruses and bacteria and will likely recognize the other potential members. This phrase could include loose genetic material, too.
You might try moving away from the word biological and towards the word organic. A prion, a virus, and a bacteria are all organic and all have the ability to replicate in the right conditions. Therefore, a phrase such as organic entity with reproductive capacity might work, but it is arguable that a virus does not have the capacity.
Best Answer
This is a very interesting question. Unfortunately, I have not been able to find enough information to give more than a partial answer. But I hope it will be of some use.
According to the Oxford English Dictionary (OED), the prefix "pro-," meaning "before," comes mainly from the Greek prefix προ-. It is cognate with the Latin preposition pro meaning "for, before, in front of," and with the English word fore. More than 60 words with this prefix were adopted into Latin in antiquity, including prologus "prologue" and propheta "prophet," so Latin has been an important intermediate source of words with this prefix.
The OED indicates that the Latin prefix prae-, which corresponds to modern English pre-, was mainly used in Classical times with verbs and verbal derivatives, or to intensify the meaning of adjectives. There are also some cases where it modifies the meaning of nouns and adjectives, but the use before a noun to indicate an earlier version of that noun apparently only became common in post-Classical Latin and later languages.
So the distinction you mention does not seem to date back to Classical languages.
It does remind me of the use of hyper- in some contexts as a more extreme version of super- (discussed in the answers to this question: Which is higher — "hyper-", "ultra-" or "super-"?). In both cases, it seems like the more common term (super- or pre-) is used for the less extreme meaning. I have not found any cases where pre- and pro- are distinguished this way outside of biology.
I found one document about biology which seems to describe a slightly different naming scheme using "pre-pre-" instead of "pro-":