It was not shown any kind of interaction between them throughout the series.
See the section above.
During the Trap Master Arc, Tenten and Shino were partnered up together. Shino used his bugs so that Tenten could cut the wire, releasing the bomb, so it wouldn't go off.
Among the FansEdit
ShinoTen isn't very popular, but has its share of fans. It is most likely shipped due to their relationship during the Trap Master Arc, and how they look together. Their rival pairings are NejiTen, ShinoHina and LeeTen.