Brace yourself for a lot of time on the tracks since the two destinations you have picked aren’t well-connected by your favoured mode of travel (I’m assuming the reference here is to the Great Rann of Kutch, for which you disembark at the railway station in Bhuj). A metre gauge line runs from Delwada (8km from Diu), but it’s only connected to Junagadh and Veraval. You’ll find seven trains plying to Ahmedabad from Veraval, the broad gauge junction closest to Diu (it’s 90km away), only one of them a somewhat convenient overnighter (Somnath Express; departs Veraval 7.35pm, arrives Ahmedabad 3.55am). You will then have to hop on to one of the seven trains from Ahmedabad to Bhuj, on average another 7.5-hour journey. Not all these trains run on all days of the week. Veraval-Rajkot-Bhuj, for example, would be a straighter route, but there are no direct connections from Rajkot to Bhuj (you’ll have to come to Ahmedabad from Rajkot, again). There are five trains from Bhuj to Mumbai, only two of which run on all days of the week, and the average journey time is 15 hours. If you have only a week to spare, I would advise a rethinking of this itinerary.
Stay at the simple Hoka Villa (from Rs 3,000), a stone’s throw from the beautiful Nagoa beach in Diu. To visit the Great Rann, it’s most convenient to stay at Dhordo (81km from Bhuj) or Hodka (84km from Bhuj). Choose between the well-maintained and aesthetic mud bhungas at the Gateway to Rann Resort (from Rs 4,000) and the Shaam-e-Sarhad Village Resort (from Rs 3,200), the latter being a worthy community-run initiative.