I strongly advise you to use an "Adafruit_GFX" style library. It would make your life easier.
However the TFT_22_ILI9225 class does have methods to suit your requirements. e.g.
void drawBitmap(int16_t x, int16_t y, const uint8_t *bitmap, int16_t w, int16_t h, uint16_t color, uint16_t bg);
So you would just say:
tft.drawBitmap(0, 0, tux, 180, 220, COLOR_WHITE, COLOR_YELLOW);
if you want to draw the solid background colour.
and
tft.drawBitmap(0, 0, tux, 180, 220, COLOR_WHITE);
if you want to draw a transparent bitmap.
Drawing WHITE text with a solid YELLOW background seems unusual. Hey-ho, it is your eyesight.
Untested. I might this later. That is how Adafruit_GFX draws bitmaps.
Adafruit lets you draw transparent text or text with a solid background.
David.