Owner only Sole Proprietor DB plan

Can a one person sole proprietor with DB plan investment in Bitcoin?  What about a one person LLC with a 401k?

As long as the Plan's Trust document allows it, sure. It's not prohibited.

Among other points to consider:

If ERISA governs the plan (which might result if there is a non-owner participant, including an eligible employee), the trustee or other fiduciary must maintain the indicia of ownership of the plan’s bitcoin inside the jurisdiction of the district courts of the United States.  ERISA § 404(b), 29 U.S.C. § 1104(b).

If the retirement plan’s sponsor, administrator, and trustee (with perhaps one human acting in all those roles) seek to maintain the plan as tax-qualified, the trustee might take steps to assure that the trustee, as the plan trust’s trustee, owns the bitcoin.  See Internal Revenue Code of 1986 [26 U.S.C.] § 401(a)(2); 26 C.F.R. § 1.401-2, § 1.401(a)-2.  Further, the trustee might take steps to assure that the trustee’s ownership of the bitcoin is within the jurisdiction of a State’s court.  See 26 C.F.R. § 1.401-1(a)(3).

The plan’s administrator and trustee might consider valuation so each Form 5500 report and each actuary’s certificate would report (or refer to) a correct value.

I would not suggest for a DBP regardless. Assuming a 415 max benefit formula for max deduction and you then get a 100% or 200% return on assets - there go your deductions, and if your near the plan's end life/termination (or owner dies) now you have excess asset and excise tax problems. Flip side, you experience a 50% or 75% loss - now your MRC jumps and plan may become unaffordable. 

If sole prop wanted to roll the bitcoin dice, I would do only in a Roth IRA or 401(k) - assuming, of course, compliance with the requirements laid out by Peter.

Thank you to all.