Besides the Vulgar Alchemy virtue, how do people go about finding new such bonuses?
There's no mechanic or rule for it in 5th Ed that I could find.
Or does the Order rely on people who do have the virtue to expand the list?
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My SG came up with this imprived version of Vulgar Alchemy:
I found it works quite well.
Bob
I have always read the core list as an example, and viewed the bonuses a natural property which makes the enchantment easier whether you know about it or not. IOW they cannot be invented. They just exist when the troupe agrees that they should exist.
Of course, this does not make the slightest bit of sense if there is a virtue to enable invention/discovery, but then it would not be the only supplementary rule that I find more confusing than useful. The core rules of the last three editions neither confirm nor reject my interpretation.
If new bonuses require invention or discovery, it seems clear that a minor Hermetic breakthrough should suffice. What other supplementary rules you can find, I do not know.
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I'd say they wait for new supplements to spell out new bonuses.
Sorry, I couldn't resist.
IIRC, there's no in-game path to that save Vulgar Alchemy.
It kinda reminds me of a discussion sparked by ezzelino about the limits of Intellego Terram, in that it depends if the bonuses are inherent to the shape/material, depend on the caster's culture, or both. So far, AFAICT, Ars Magica has followed the first road (although you may argue that the OoH is a single, common, culture)
Okay, it's the afternoon, it's hot, I'm losing track already 
What I mean is it all depends on how it works in your campain, and how your troupe wants to to it.
If they are already there, you may just try "blindly" new shapes or materials, with you SG assigning invisible bonuses, and you trying to find out the value of the bonus by experimentation.
But it may be that a bonus doesn't come from the S&M but from magical practice. Or a mix of both.
The idea is that, per se, a ruby does nothing to Fire Magic. But someone, using something like Vulgar Alchemy, experimented on rubies and found a small set or rituals, of a special way to concentrate, that enables it to focus fire magic. And then, the knowledge spread through the order. It was a ruby because it felt appropriate (and it probably helped), but, theoretically speaking, you could do the same with a cup of water
Going back to the fixed/intrinsic bonus.
You could assume that your character knows, or can pretty well guess, what can improve some magics.
So you'd ask your SG "I want something that improved Binding magics", she'd ask you for, say, a Philosophiae/AL/MT roll (or the lowest of the 3), and, if you succeeded, she'd say "you figure that a rope will add +3". You could then pass the knowledge, without other magi having to do the roll. Especially as this roll could require spending a season of research and pondering.
As others have pointed out there is only Vulgar Alchemy as a published rule that allows players to come up with new bonuses in a reliable and predictable way.
However I have never interpreted the published list to be exhaustive. Neither the one in the core book nor if you include everything from supplements. To me these are examples meant to guide you onto the right mindset for coming up with new bonuses.
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It is consistent with the published shape and materials bonus that those depend on tradition and knowledge, and being able to invent new S&M on the fly is very much a house rule - although an arguably common and convenient one. We do have bonuses conditional on reading Sefer ha-bahir, for example, which includes additional bonuses for common shape and materials such as amethyst, silver, agate just as there are shape and material bonuses dependent on an additional virtue, like craft magic.
Absolutely. Nobody contradicted that. If you mean to imply that the opposite reading, that S&M bonuses are just there to be used whether you know or not, is inconsistent with the published core ruleset, then I would love to see the citation.
It is one that we apply in our group.
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In our saga, we decided that Vulgar Alchemy had been integrated and was available in a recent Bonisagus Folio.
Integrated Vulgar Alchemy:
During any seasonal activity which uses Shape and Material bonuses (enchanting items, potent spells) a maga can develop a new Shape & Material bonus.
The troupe will determine the maximum bonus a Shape or Material can provide and players must track what Shapes and Material Bonuses they have developed.
During a season, a maga can learn to incorporate up to her (Magic Lore / 3) of that bonus. Thus, after one season of work, a maga with Magic Lore 6 could develop a new Shape or Material bonus of +2. In a second season, if the Shape or Material had a higher maximum bonus, that same maga could develop a Shape or Material bonus of +4. During lab activities over multiple season, the maga can only use the bonus learned from their first season (the lowest bonus).
Once the maximum bonus is developed by a maga, she can share that knowledge with others. By writing a tractatus on Magic Theory or Magic Lore, a maga can include the knowledge of one Shape or Material bonus. In a Summae, the maga can include knowledge of (2 x {Magic Lore / 3}) Shape or Material bonuses. A labtext can include knowledge of all the S&M bonuses used in the project.
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Is the (2* (magic lore/3)) the total bonus to be shared, or the total different S&Ms you can share?
For example, if you have Magic Lore 6, can you share a total of +4 bonus? Or a total of 4 Shapes and Materials
In a summa, that is the number of shape and material bonus. The magnitude of those bonus is irrelevant. In your example that would be 4 Shape and Material bonuses
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To me the bonuses are not limited and so new ones can be created with little effort or additional time. I do not see the Vulgar Alchemy virtue as needed to create new bonuses.
As for mechanic, well, I guess you could do it as part of the enchantment process. Maybe make it more difficult the first time but then once its known its as easy as the others. Though I don't think its necessary to add that.