I know of no public transportation between StJ an StX. There are a couple of choices between StT and StX.
This is from the St. Thomas / transportation link above the messages.

https://www.vinow.com/general_usvi/interisland_ferry/#stcroix

St. Croix Ferry: Christiansted, St. Croix - Charlotte Amalie, St. Thomas
This ferry departs from the Marine Terminal in Gallows Bay on St. Croix and the Marine Terminal in Charlotte Amalie (next to Seaplane Terminal) on St. Thomas. Arrival should be at least 45 minutes prior to departure. Photo Id required.
Smith's Ferry Service
Rates: Adults/$50 one-way, $90 roundtrip. Children 3-11/$45 one-way, $80 roundtrip. Children under 2 years old/$10 one-way, $20 roundtrip. Telephone: (340) 775-7292
Time: 90 minutes.

Leaving Gallows Bay, St. Croix
Fri, Sat, Sun, Mon
7:30am
4:30pm

Leaving Charlotte Amalie, St. Thomas
Fri, Sat, Sun, Mon
9:30am
6:45pm

https://www.vinow.com/general_usvi/interisland_airtravel/

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(508) 771-6944
(800) 352-0714
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Thank you for the information. I was hoping for a direct route but I see that I must go to St Croix via St Thomas from St John.

The seaplane between STT and STX is very popular:

www.seaborneairlines.com

If you opt for the ferry, do 'phone beforehand as they're not renown for being totally reliable. Also be advised that the crossing can be quite rough and it's often locally referred to as, "the barf barge!"

Thank you for that information. I think I'll skip the 'barf barge' and opt for the seaplane.

You can book both the ferry & plane through Seaborne. We did a daytrip from STX to STJ, they held the ferry for us when the "de flyboat be comin' late '