Naseeb Shaheen's Biblical References in Shakespeare's Plays is a marvelous reference work for exactly what its title says. Do you want to know more about what Hamlet means when he refers to Polonius as Jephthah? Shaheen will point you toward Judges 11:30–40. Not only that, but he'll tell you what the Homily Against Swearing and Perjury has to say about it:
It's a wonderful and helpful resource. And that makes it a rare event indeed to spot something not in Shaheen. But I think I've found one.
I recently found the phrase "a wave of the sea" in a recent translation of the Bible, and it immediately made me think of Florizel's speech to Perdita in The Winter's Tale. In a wonderful speech about Perdita's virtues and beauties, he says,
What you doStill betters what is done. When you speak, sweet,I’d have you do it ever; when you sing,I’d have you buy and sell so, so give alms,Pray so, and for the ordering your affairs,To sing them too. When you do dance, I wish youA wave o’th’ sea, that you might ever doNothing but that, move still, still so,And own no other function. (IV.iv.135–43)
The delightful image is of the perpetual movement of the waves, always the same but ever varied in their beauty.
The passage from James is a little different. Here's James 1:5–6 from the Geneva Bible of 1560:
If any of you lacke wisedome, let him aske of God, which giueth to all men liberally, and reprocheth no man, and it shalbe giuen him. But let him aske in faith, and wauer not: for hee that wauereth, is like a waue of the sea, tost of the winde, and caried away.
The image here is more negative. The faithful are advised not to be like a wave of the sea, which is not solid and lasting like faith is meant to be.
If this is a biblical allusion (and I'm entirely open to it not being so), it's a complicated one. Florizel would want Perdita to be solidly faithful to him (i.e., not like a wave o'th' sea), but does want her to be infinite in variety while still the same in her essentials . . . at least while she's dancing.
Bonus Image: The Page from Shaheen's book where these passages could have been addressed: