"Mg-Fe-orthoamphibole" would include the entire [anthophyllite]-[ferro-anthophyllite] and [gedrite]-[ferro-gedrite] series, but would exclude the possibility of the [tremolite]-[ferro-actinolite] series (these would be "Ca-clinoamphibole", although the "clino" could be considered redundant because there are no calcic orthoamphiboles). "Asbestiform" could be added as a descriptive modifier, which would inform viewers of your specimen that from among all the amphibole species, yours is presumably one of the roughly half-dozen or so known species that has been reported in an asbestiform habit (there are a few others not included in the preceding discussion).

This "what particular species of a complex solid solution is my sample?" issue isn't unique to your specimen, of course. Even just anyone who has common "hornblende" in their mineral collection is faced with a similar dilemma, since "hornblende" is no longer a mineral and the collection of species considered under the "hornblende" umbrella could be any of (or even zoned multiple) compositions representing perhaps a couple dozen species.

In lieu of sending your specimen out to a commercial lab for analysis ($$) or taking it to your local university or museum for analysis (also possible, depending on their willingness to engage in public outreach on such matters), it's also possible collectors from a local club may be able to offer a more definitive ID, based perhaps on their own independently analyzed specimens of essentially identical material (presumably somebody was curious enough to do so). Another possibility is just reviewing the scientific literature on the deposit... it may turn out from the reports that the tremolite/actinolite from there is commonly asbestiform but the anthophyllite never is (or vice versa?).  Some of these reports may also contain analytical data, descriptions of assemblages (maybe one species is only found with quartz there while the other is only found with calcite there?), and photos of specimens... all potentially helpful tidbits of information.

I suppose your specimen would qualify as "byssolite" and you can add that name to the locality if you'd like (and if your membership level doesn't give you the ability to add minerals to a locality, let me know and I or someone else with the ability can add "byssolite" for you).

But as others here sometimes make a bit of light-hearted fun with me about, I'm not a big fan of varietal names for minerals and tend to prefer to see the names of species and series and such. But this case might be an exception, because while "byssolite" tends to be thought of as typically being part of the tremolite-actinolite series, the name may encompass other pale-colored furry amphiboles as well. And since there was some question earlier as to which particular series your furry amphibole may actually belong to, "byssolite" may indeed be the best choice to cover that ambiguity.

 yes, that is correct, but I don't know at what minimum Fe concentration along the Mg-dominant to Fe-dominant join that observation begins to hold true, so I don't know if it necessarily helps you to decide whether to add a "ferro-" prefix or not.

(as a fun aside, Ni- and Co-rich compositions might also be expected to fuse into magnetic little balls, but these aren't currently known in nature).

Just a little background here:

If you click on the amphibole supergroup link on the byssolite page, you'll get a more detailed overview of what elements typically occur in what sites. But to summarize, "byssolite" may quite likely have some Fe in it. But we just couldn't give it a more detailed formula because "byssolite" isn't a specific mineral, but just a collector's name for a whole family of furry amphiboles, some of which might have some Fe and some that probably don't.