Prelim: I am no expert on implementation techniques or the frontier of what gate technology is being used in current renditions of Trapped Ion QC.
The Molmer-Sorensen gate is generally what is used in Hot Trapped Ion QC since it does not require the phonon mode of the Ion trap to be in the ground state; this gate forms a universal set of gates.
The gate operates by 'physically rotating the Qubits' (loosely), and through those operations applied at different times we can trivially obtain the SWAP and also C-NOT, C-Z, etc. So it's not a question of 'either rotate the bits or apply the SWAP gate', since the rotation is itself the SWAP gate.
Now if we are using other types of gates, like the Cirac-Zoller gate; then yes we would have to apply the gate in different ways to obtain the SWAP operation (Cirac-Zoller is just a C-NOT so this is quite trivial), and if we only have access to the Cirac-Zoller gate then there is no way to 'rotate' the Qubit. It is all a question of what tools are available for the technology you are working with.