Potential for damage to wheels depends on sharpness of the bump, speed, bike and rider weight, tire volume and pressure, and how tough the wheels are.

Moving your weight back or pulling up on the bars will lessen the impact to the front wheel but will increase impact on the rear.

Large or sharp bumps are best avoided altogether. Standing on the pedals with bent knees and lifting your butt off the seat a little will allow the bike to move underneath you and absorb the impact.

You can also move your weight back as the front wheel goes over the bump then move weight forward as the back wheel goes over, but this gets harder to do as speed increases.

Hitting any obstacle with the front wheel has always a worse events development potential compared to hitting the same obstacle with the rear wheel: one can loose control over the bicycle and fall down. Achieving the same result after a hit in the rear wheel is also possible, but much less probable (however, another possibility to be thrown out of saddle if one sits too tight on it arises). Even if the rear wheel skids or destroys itself, you will still regain much of control so that you are more likely to make a controllable stop.

Because of this, if no other alternative is available (braking, avoiding, hoping over etc.), I would recommend lifting the front wheel. If, after the wheel is over the obstacle and you still have reaction to unlift some weight from the rear wheel, do it. Doing so will help the rear wheel to bump over the obstacle and minimize risk of wheel damage. If you do not do that, it is fine as long as you are not sitting fully on the saddle. Otherwise the rear wheel bump will have chance to throw you into air. Standing on the pedals is recommended during the whole time of attack.

I feel like I don't feel so much the bump

It is actually good that you do not feel the bump — it means you have overcome it without creating a risk to loose control. If you were standing on pedals, it were your legs that absorbed the bump for you. If you sat fully on your saddle, the whole kinetic energy change caused by the bump would have been transfered to your center of mass, effectively launching your whole body into flight.

if I do that but what matters is if I'm damaging the wheels.

Yourself avoiding undesired flight matters more than your wheels. Wheels are built to withstand bumps, do not think about them too much.

For sharp-edged bumps it is better not to hit them "head-on" with either wheel. In that case, a bunny hop to get both wheels over without contact is best. If the bump is somewhat rounded it probably doesn't matter if you roll over it or jump over it and land the wheels from the air.