The poems from The Adventures of Tom Bombadil give us some insight about both Tom and Goldberry.
Indeed Goldberry is a River-woman's daughter. As was previously mentioned, Goldberry makes an attempt to 'catch' Tom - she grabs him by the beard and he falls into the water, but releases him and swims back to her mother's house after some scolding. She leaves no impression whatsoever of having been romantically interested in Tom. In fact, after this, Old Man Willow and then Badgers also try to catch him. The Great Willow does this in the same manner as later he does it with the hobbits:

Up woke Willow-man, began upon his singing,
sang Tom fast asleep under branches swinging;
in a crack caught him tight: snick! it closed together,
trapped Tom Bombadil, coat and hat and feather.

But all Tom does is demands to be let out, and is obeyed immediately. Likewise Badgers that brought Tom inside their tunnels (he was hiding from rain in one of their holes) get a reprimand like this and set him free right away (and definitely feel ashamed):

Now, old Badger-brock, do you hear me talking?
You show me out at once! I must be a-walking.
Show me to your backdoor under briar-roses;
then clean grimy paws, wipe your earthy noses!
Go back to sleep again on your straw pillow,
like fair Goldberry and Oid Man Willow!'
Then all the Badger-folk said: 'We beg your pardon!'
They showed Tom out again to their thorny garden,
went back and hid themselves, a-shivering and a-shaking,
blocked up all their doors, earth together raking.

Then Tom is 'greeted' by Barrow-wight who was waiting for Tom in Tom's house. He too fails to catch Tom.

Hoo,Tom Bombadil! Look what night has brought you!
I'm here behind the door. Now at last I've caught you!
You'd forgotten Barrow-wight dwelling in the old mound
up there on hill-top with the ring of stones round.
He's got loose again. Under earth he'll take you.
Poor Tom Bombadilt pale and cold he'll make you!'

'Go out! Shut the door, and never come back after!
Take away gleaming eyes, take your hollow laughter!
Go back to grassy mound, on your stony pillow
lay down your bony head, like Old Man Willow,
like young Goldberry, and Badger-folk in burrow!
Go back to buried gold and forgotten sorrow!'

Out fled Barrow-wight through the window leaping...

I think that given the time this particular poem was written (1934; long before LOTR), it is very interesting to see Barrow-wight in existence already - the history of Barrow-downs wasn't invented yet and the significance of Barrow-wight wasn't at all as great as it has become later.
And so when it is said that no one has caught Tom, the meaning is not that nobody tried (as his outward appearance doesn't impress anybody), but that he cannot be kept - all recognize him as someone they must obey, but not until he speaks to them.

Goldberry is simply physically caught by him. Tom doesn't talk much to her about his love or anything of this sort. He just says that in the pools she will find no lover! Makes me laugh that he presents himself as a lover. (Well shouldn't there be some sort of a father to Goldberry, and conceivably other male river-folk?). She seems to say nothing in return... She acquiesces and that's it. I was thinking of all this as just some fairy tale, which ATB really is... Nothing to give much thought to. Then I recalled the piece from the Lay of Leithian where Beren and Luthien met in spring.

...He leapt towards her as she stayed
And caught and kissed that elfin maid.
As love there woke in sweet surprise,
The starlight trembled in her eyes...

Interesting (and similar) take on love!

Back to Tom, River-woman was sighing and Barrow-wight crying the night of Tom's wedding... I wonder if there is any significance to that?

On a very different note, Goldberry's name is pretty interesting, given that she is some sort of a water spirit. There are no berries under water, are there?

And just a couple of words on Tom and Farmer Maggot. I was wondering who visited whom? Tom seems not to go much beyond his Old Forest, and hobbits in general are afraid of that forest. From the poem Bombadil Goes Boating it appears that Tom visited the Shire and exchanged tidings with Farmer Maggot. Of course this is an externally later poem, and the mention of many LOTR things there is not surprising.