If your campaign is low on discrete combat encounters then there will be little you can do to force characters to ration resources between short/long rests.
But you can extend encounters by having creatures try to flee, or one fight rolls into another one. This can make combat last longer than some spells/abilities (like Barbarian Rage), forcing characters to have to spend more resources, or choose to do without. But Wild Shape is a tough one since it lasts quite a long time (1/2 level in hours) so unless you can force the druid to shift back into normal form it will last longer than any single encounter.
Another option is to trick characters into thinking there is going to be combat, so they engage all their pre-combat abilities, but then nothing happens (combat related, anyway). But this is a low trick and would only be acceptable one or twice, IMHO.
Another possibility is to ambush characters, so that they would have to spend their action activating an ability (unless the druid has combat wild shape) or doing something else. This drives characters towards the economy of actions and they have to prioritize. Again, this would be an exception to normal encounters.
In general however, it is difficult to drain resources in 5e unless you also limit short/long rests. Allowing characters to rest while in a dungeon will definitely skew the difficulty curve in favor of the characters since they can refresh many abilities and HP. So you will need to apply pressure on the parties ability to get rest, rather than upping the encounter frequency hoping the party uses expendable resources.
But it seems like you feel the druid wild shape ability is overpowered, or at least is that characters "go to" option. Given the number of times (2) and the length (hours) it can be used, it is clearly a core competency of the druid, so I wouldn't try to deny the player access to it. Instead focus on what it prevents the character from doing. Open a door? Probably not. Give another character a potion? Nope. No spell casting. No item use. No ability to converse (outside of magic). So have the player play that way. He can't engage the other players outside of animalistic grunts and gestures. Design encounters that would appeal to the druids abilities other than shape change.
Why is combat too easy? Is the party just that well coordinated? Are enemies not using their special abilities, instead just standing around to be damage sponges for the players? Can the players choose all of the encounters, are they never ambushed or trapped? Keeping the players guessing, so they never know if that one goblin is actually super tough, just the bait for a trap, or maybe really is lost by himself is key to resource management.
Uncertainty in combat usually drives players to conserve resources instead of going nova on everything right off the bat. Forcing hard decisions about resting is key as well. Doesn't have to be "rest and get attacked", it can be "rest and that goblin band slips away", or "rest and the monsters have time to move part of their treasure horde" or "rest and another villager gets eaten". Let the party make the decision, you just lay out the choices and the consequences.