It would still wind up in the liver. In a 1966 paper -- "the metabolism of intravenously injected isotopic cholic acid in Laennec's cirrhosis," by Blum et al. -- it was discovered that "when isotopic cholic acid was administered intravenously to normal subjects, there was a rapid and permanent disappearance of isotope from the systemic plasma, reflecting the essentially complete localization of bile acids in the liver, biliary apparatus, intestinal content, and portal blood."

Bile acids might be less toxic if administered via IV infusion, in comparison with oral administration. Then again, they might be more toxic. (Due to rapid excretion or poor absorption via the oral route.) I don't know offhand if one delivery method or the other would be preferred in this regard.

But though most bile acids are toxic, not all of them are. TUDCA and UDCA are not only liver-safe, they're first-resort drugs for resolving drug-induced liver damage and promoting liver health. If these "healthy bile acids" can combat MS, that would be a very interesting result. TUDCA and UDCA are very cheap, and their safety profiles are well established.