I thought it might be possible to do it with formulas and in the end I think it is but Numbers is very strange and inconsistent and buggy when it comes to text formats and formulas. After some trial and error here is a possible solution.
cell A1=CODE(10)
This is a line feed character. We want to search your strings for it but you cannot put that character directly into the FIND formula, you have to reference a cell that contains this character.
C2=LEFT(B2,FIND($A$1,B2))
D2=RIGHT(B2,LEN(B2)−LEN(C2))
E2=C2&D2
Then select column C and format it as bold. Hopefully it will result in what you see in my screenshot.
Now, to get it back into column B complete with the formatting, you have to do a roundtrip through TextEdit.
Select all the cells in column E
Copy
Open TextEdit
Paste
Manually select the columns of text (not including any additional line(s) TextEdit adds to the beginning and end)
Copy
Go back to Numbers
Paste into column B
For those wondering what I am finding inconsistent, here is an example
cell A1 has text all of which is formatted as bold
cell A2 has the formula =A1
The text is correct in A2 but the format does not carry over, it is regular text
But then put some regular text in cell A1 along with the bold text, now the formatting comes across to A2
There is also bugginess where formats might come over but, if you change the format, it no longer does. I can't remember exactly what I was doing to get this to happen but it was annoying.