The camera's I use only support RAW and JPEG.

Oh, well nevermind on that then. Some camers do in fact allow for TIFF's instead of RAW.

I am not sure if there is a way to shoot in TIFF directly with the same information quality as RAW?

My point being that you have the most latitude in adjustment directly with the raw, rather than the TIFF. You should be making adjustments first, and then converting to TIFF, not the other way around. Converting form RAW to JPG and then doing all your editing is bad for the same reason (just to a greater extent).

I have looked at Lightroom but it didn't seem to offer more then Bridge/Photoshop offers

There's a reason those 2 (Lightroom / Capture One) are the industry standard (in addition to Photoshop). Lightroom is bridge + most photo related assets of Photoshop streamlined in to one package.

What put me off about Lightroom is the lack of retouching possibilities compared to Photoshop

It's to be used with Photoshop, not as a substitute for it. That being said, for a lot of people, it is actually a substitute.

The file structure was set up to ensure a non-destructive but logical workflow with back-ups

All adjustments in LR/C1 are also non-destructive. You can also save the adjustments you've made and make multiple versions of the same file. My LR imports automatically backup to a secondary drive too.

However if you think Lightroom can add something to the workflow like a decent batch color-correction I am open to consider it.

Well, batch correcting RAW's will yield better results than batch correcting TIFF's.

I do LR for importing, sorting, ratings, basic adjustments. Then convert to TIFF and fine tune in Photoshop.