diff --git a/src/Bridges/lazy_bridge_optimizer.jl b/src/Bridges/lazy_bridge_optimizer.jl
index 37255c56b9..0b25e67987 100644
--- a/src/Bridges/lazy_bridge_optimizer.jl
+++ b/src/Bridges/lazy_bridge_optimizer.jl
@@ -255,7 +255,9 @@ function node(
     @nospecialize(b::LazyBridgeOptimizer),
     @nospecialize(S::Type{<:MOI.AbstractSet}),
 )
-    # If we support the set, the node is 0.
+    # If we support the set, the node is 0 unless the inner model reports a
+    # non-zero `VariableBridgingCost` (which can happen when the inner model is
+    # itself a bridge optimizer that needs to bridge `S`).
     if (
         S <: MOI.AbstractScalarSet &&
         MOI.supports_add_constrained_variable(b.model, S)
@@ -263,7 +265,22 @@ function node(
         S <: MOI.AbstractVectorSet &&
         MOI.supports_add_constrained_variables(b.model, S)
     )
-        return VariableNode(0)
+        inner_cost = MOI.get(b.model, MOI.VariableBridgingCost{S}())::Float64
+        if iszero(inner_cost)
+            return VariableNode(0)
+        end
+        # The inner model supports `S` but with a non-zero bridging cost.
+        # Create a leaf node whose distance is `inner_cost` so that bridges
+        # that emit constrained variables in `S` account for it.
+        cached = get(b.variable_node, (S,), nothing)
+        if cached !== nothing
+            return cached
+        end
+        new_node = add_node(b.graph, VariableNode)
+        b.variable_node[(S,)] = new_node
+        push!(b.variable_types, (S,))
+        b.graph.variable_dist[new_node.index] = inner_cost
+        return new_node
     end
     # If (S,) is stored in .variable_node, we've already added the node
     # previously.
@@ -315,9 +332,27 @@ function node(
     @nospecialize(F::Type{<:MOI.AbstractFunction}),
     @nospecialize(S::Type{<:MOI.AbstractSet}),
 )
-    # If we support the constraint type, the node is 0.
+    # If we support the constraint type, the node is 0 unless the inner model
+    # reports a non-zero `ConstraintBridgingCost` (which can happen when the
+    # inner model is itself a bridge optimizer that needs to bridge `F`-in-`S`).
     if MOI.supports_constraint(b.model, F, S)
-        return ConstraintNode(0)
+        inner_cost =
+            MOI.get(b.model, MOI.ConstraintBridgingCost{F,S}())::Float64
+        if iszero(inner_cost)
+            return ConstraintNode(0)
+        end
+        # The inner model supports `F`-in-`S` but with a non-zero bridging cost.
+        # Create a leaf node whose distance is `inner_cost` so that bridges
+        # that emit `F`-in-`S` constraints account for it.
+        cached = get(b.constraint_node, (F, S), nothing)
+        if cached !== nothing
+            return cached
+        end
+        new_node = add_node(b.graph, ConstraintNode)
+        b.constraint_node[(F, S)] = new_node
+        push!(b.constraint_types, (F, S))
+        b.graph.constraint_dist[new_node.index] = inner_cost
+        return new_node
     end
     # If (F, S) is stored in .constraint_node, we've already added the node
     # previously.
diff --git a/src/Utilities/cachingoptimizer.jl b/src/Utilities/cachingoptimizer.jl
index f3392bbf07..0df5e5863f 100644
--- a/src/Utilities/cachingoptimizer.jl
+++ b/src/Utilities/cachingoptimizer.jl
@@ -897,6 +897,16 @@ function MOI.get(model::CachingOptimizer, attr::MOI.AbstractModelAttribute)
     return _get_model_attribute(model, attr)
 end
 
+function MOI.get(
+    model::CachingOptimizer,
+    attr::Union{MOI.VariableBridgingCost,MOI.ConstraintBridgingCost},
+)::Float64
+    if state(model) == NO_OPTIMIZER
+        return MOI.get(model.model_cache, attr)
+    end
+    return MOI.get(model.optimizer, attr)
+end
+
 function MOI.get(
     model::CachingOptimizer,
     attr::MOI.TerminationStatus,
diff --git a/test/Bridges/General/test_lazy_bridge_optimizer.jl b/test/Bridges/General/test_lazy_bridge_optimizer.jl
index 2d28d77a45..a2b0d90a21 100644
--- a/test/Bridges/General/test_lazy_bridge_optimizer.jl
+++ b/test/Bridges/General/test_lazy_bridge_optimizer.jl
@@ -2477,6 +2477,46 @@ function test_issue_2870_relative_entropy()
     return
 end
 
+MOI.Utilities.@model(
+    NonnegOnlyModel,
+    (),
+    (),
+    (MOI.Nonnegatives,),
+    (),
+    (),
+    (),
+    (MOI.VectorOfVariables,),
+    (MOI.VectorAffineFunction,)
+)
+
+function test_nested_lazy_bridge_optimizer_cost()
+    # When the inner model is itself a `LazyBridgeOptimizer` that needs to
+    # bridge a set, the outer `LazyBridgeOptimizer` must take the inner
+    # bridging cost into account when computing edge costs in its own graph,
+    # not assume zero cost just because the inner reports `supports`.
+    T = Float64
+    # Solver supporting only `Nonnegatives`-constrained variables.
+    inner = MOI.Bridges.LazyBridgeOptimizer(NonnegOnlyModel{T}())
+    MOI.Bridges.add_bridge(
+        inner,
+        MOI.Bridges.Variable.NonposToNonnegBridge{T},
+    )
+    @test MOI.get(inner, MOI.VariableBridgingCost{MOI.Nonnegatives}()) == 0.0
+    @test MOI.get(inner, MOI.VariableBridgingCost{MOI.Nonpositives}()) == 1.0
+    cache = MOI.Utilities.CachingOptimizer(
+        MOI.Utilities.UniversalFallback(MOI.Utilities.Model{T}()),
+        inner,
+    )
+    @test MOI.get(cache, MOI.VariableBridgingCost{MOI.Nonpositives}()) == 1.0
+    outer = MOI.Bridges.LazyBridgeOptimizer(cache)
+    @test MOI.get(outer, MOI.VariableBridgingCost{MOI.Nonpositives}()) == 1.0
+    @test MOI.Bridges.bridging_cost(
+        outer.graph,
+        MOI.Bridges.node(outer, MOI.Nonpositives),
+    ) == 1.0
+    return
+end
+
 end  # module
 
 TestBridgesLazyBridgeOptimizer.runtests()