First, I went to a table of bond energies and checked. I’m not too worried about the particular number, but yours seems to be a bit high.

The specific problem you are having is that you haven’t got the right reaction mechanism; in this particular reaction type, called S_N2, the C-OH bond forms at the same time that the C-Br bond breaks, so it “donates” some energy to the activated complex and reduces its overall energy. But you also have some conceptual problems: these tables of bond energies simply cannot be used in this way.

Bond energies in these tables are for so-called “homolytic" cleavages in which there is no separation of charge. If you use the bond energies as they were intended, to predict an overall reaction energy, that wouldn’t matter. Thermodynamics guarantees that you will get something quite close to the actual overall reaction enthalpy no matter how you arrive at it; if you go by a higher-energy pathway (homolytic cleavage) you are returned more energy by the homolytic reformation of bonds.

But you can’t use bond energies to arrive at activation energies for a particular reaction, because activation energies—unlike overall reaction energies—are sensitively dependent on the way you get from point A to point B. And in the reaction you are concerned with, you definitely don’t get there by homolytic bond cleavage!

Think of it this way: an overall reaction energy, and the bond energy tables from which you can calculate it, are like a table of city elevations. It tells you that Albany is on higher ground than New York. But it doesn’t tell you the best way to get from one to the other.

An activation energy measures the lowest-effort way to get from Albany to New York; you go down the Hudson Valley, not through the Catskills. (And you need a different tool to tell you this: not a table of elevations, but a topographic map.)

The only valid way you could use these tables of bond energies to estimate activation energies is if you also knew that the reaction actually proceeded by homolytic bond cleavage, as some free- radical reactions do. Try using your table of bond energies to estimate the activation energy for free-radical bromination of methane… (And even there it might not work, because there are simultaneous bond forming/bond breaking steps in that reaction, too.)