Slepian Inequality for Brownian/Gaussian Bridges

Question

I am trying to find any reference related to understanding bounding probabilities of generalized Brownian Bridges. The motivation comes from Slepian's inequality/lemma, which specifically states that for two zero-mean Gaussian processes $S_1$, $S_2$ with covariance functions $K_1(t,\tau)\leq K_2(t,\tau)$ for all $t,\tau$ and $K_1(t,t)=K_2(t,t)$ for all $t$, then for any fixed bound $f(t)$ on $[0,1]$: $$\mathbb{P}(\forall t\in [0,1] \;\; S_1(t)\geq f(t))\leq \mathbb{P}(\forall t\in [0,1] \;\; S_2(t)\geq f(t))$$ I am wondering if there are any similar results for the bridges of these processes, i.e. consider $B_1(t)=S_1(t) \mid S_1(1)=0$ and $B_2(t)=S_2(t)\mid S_2(1)=0$, can we somehow compare: $$\mathbb{P}(\forall t\in [0,1] \;\; B_1(t)\geq f(t))\; ? \; \mathbb{P}(\forall t\in [0,1] \;\; B_2(t)\geq f(t))$$ It is clear that the general form of Slepian's inequality is not true for the "bridges" (e.g. consider $S_1$ as Wiener process and $S_2(t)=tW_1$ where $W_1 \sim N(0,1)$ and take any $f(t)$ positive), but are there partial results anywhere? Any pointers to relevant references would be kindly appreciated.