I have these two separate strokes - how would I go about connecting them perfectly, so there is no bend where they meet?
You can select both endpoints with the direct select tool (A) and then do Command (or Control)-Option-J to Average the points (the default selection of Both usually works for me). Then Command (or Control)-J to Join the points.
If the anchor points are from different paths you can do this:
1) Select the 2 end-points with the direct select tool (A).
2) At the top bar under the anchor section, select Connect Selected End Points
.
You can then delete one of the anchor points and adjust the curve.