As a compromise action for bottleneck and fingerstyle I usually aim for 3.5mm on the bass side and 3mm on the treble at the 12th. The nut I do by eye, I've never measured it, but it tends to be just a touch higher than the optimum fingerstyle setup - pretty much as factory guitars usually come straight out of the box.
For pure bottleneck you might want to look at at least 4 on the bass, 3.5 on the treble but it also depends on your string gauges and the weight of the bottleneck you're using. Stiffer strings - say .015 to .056, which is what I usually go for - or a lighter slide will take a lower action than .012s and a heavy brass slide.
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