Iron is expected in the form of FeO. Once it comes to Ba, it is also possible due to fact MgO and CaO are both expected, however Ba, most likely in the form of BaO should be very less in concentration.
Bentonite is an argillaceous rock with predominantly smectite-group phyllosilicates. There are two smectite group minerals which can accommodate either bivalent or trivalent Fe in their lattice. Saponite (trioctahedral) can substitute bivalent Fe for Mg and dioctahedral nontronite con accommodate trivalent Fe in its structure. The first one signals reducing, the second one an oxidizing environment of formation.
Barium can be expected to have entered bentonite, e.g., as a heavy mineral (barite) or through other K-bearing phyllosilicates which can show up as minerals of their own, e.g., illite or vermiculite or as mixed-layers. Bivalent Ba can substitute for monovalent K in these minerals. My comments are based on a consideration of the clay mineralogical lattice parameters only. For a more a detailed information of mine it has to be provided some data on the true nature of your bentonite.
Is it supergene or hypogene or a mixture of the two processes?
A bentonite is normarly mainly composed of 70-80 wt.% montmorillonite, where most of the Iron (generally > 80%) is found (as octahedral structural Fe(III)). Some structural Fe(II) may be found in accessory clay minerals (illite, micas). In addition, bentonite generally also contains various Fe(II/III)-bearing accessory oxides, hydroxides and sulfides (usually few wt.%, sometimes more) which can include: goethite, hematite, magnetite, ilmenite, pyrite, siderite. This depends on their origin and history.
I personally don't consider clay rich material with more than 10 wt.% Fe (such as Rokle or Asha) as bentonites.
Barium contents of bentonites is generally very small.
It is for instance below 0.2% in Ibecoseal bentonite, where few large (up to mm size) grains of barite can be found. Some can be found in clays interlayers, as exchangeable cations, but contents are usually very limited (