I have been in a similar situation. My employer was sending me to a conference that began Sunday morning; no Sunday-morning flight would get me there in time for the start and no Saturday-night flight left late enough after the end of Shabbat.
I explained the difficulty to my manager and asked to travel on Friday afternoon. (They'd assumed I would travel on Saturday, so the issue was one extra hotel night, same as for you.) I said I was willing to stay in a less-expensive hotel nearby, which I think demonstrated that I was willing to do some work or accept some inconvenience. (I did not offer to pay for it.) The expense was approved and my manager said not to bother changing hotels.
So my recommendation to you is:
Know what your backup plan is if the answer is no. (Mine was to travel Sunday morning and miss the opening of the conference.)
Explain the problem to your manager, who is presumably unaware of the problem. Even if he knows you observe Shabbat, he might not understand what that means -- that it has strict time limits and that its restrictions include travel.
Ask if, given the circumstances, the company will pay for an extra room night. If you can offer any mitigation (different hotel, finding a cheaper flight to compensate, etc), do that. Make it clear that it's a request, not an expectation.
If the answer is no, proceed with your backup plan.
Your company almost certainly doesn't have to provide this accommodation -- but they value you enough to employ you and send you to this conference and they may well see the small cost of a hotel-night as just part of the cost of doing business. It doesn't hurt to ask.
In case you're wondering, I went to a university Hillel for services, found local hospitality for meals, made suitable donations later, and didn't expense that.