John,
I haven't seen a Strat with Bigsby, but of course Telecasters have had models with Bigsby for those who want them. I suppose that putting one on a Stratwould not be any different, but I suppose it also comes down to personal taste -I would simply get a normal tremolo Strat if we are talking 6 string, but perhaps you are thinking of a 12 string with Bigsby? I know that Rickenbacher and maybe Gibson have made guiatrs like that, but perhaps the views expressed in this discussion group here might be of some guidance:
http://acapella.harmony-central.com/arc ... 81906.html
Regards
By the way, here's a pic of a Ventures model Mosrite 12 string, not Bigsby but similar.