Hallow Dear,
I appears from your history that both of you have newly started your sexual life. At the outset let me congratulate you for that.
I will answer your queries reverse way.
What you are suspecting about the bleeding she had after (or may be during sex) is most likely due to defloration wherein the
hymen gets ruptured during first (or may be initial few) penile entries is right. Hymen is a fibromuscular septum present at the opening of the vagina. It usually gets ruptured during the initial intercourses in life; however it may get ruptured by some non-sexual causes like riding a two wheeler, climbing trees, sitting astride, athletics, etc.. I feel you need not worry about this bleeding.
Most of the women are very apprehensive about the entry of the penis into the vagina because they are not aware of the distensibility of vagina. Hence they contract their vaginal muscles in the anticipation of pain which creates a resistance to penile entry. Also, dry handling of the female genital organs is uncomfortable and painful. You should also keep in mind that for first few months to year(s) complete penis does not entre into vagina during intercourse.
I would suggest you following tips to get over these problems:
1. Spend good amount of time in sexual foreplay to arouse your partner sexually.
2. Do not insert the penis in to vagina till there are good amount of vaginal secretions. In fact, it is always a good practice to wait till she demands the insertion.
3. Use of lubricants will facilitate easy and free entry in to vagina. You would not have to use force to entre the vagina. This will minimize pain. Please do not use oil-based lubricants like oil, Vaseline, soap, etc. They are harmful to women's genital organs and to condom also. Always use water-based lubricants. Vaginal jellies available in the market are very good for this purpose.
4. Explain her all these facts and win her confidence. Assure her that with all this, she is not going to feel much pain. She should relax while you are inserting the penis. In fact, it is a good practice that she takes deep breaths by open MOUTH while the penis is entering the vagina. This prevents the vaginal muscles contractions.
I am sure you will overcome all the difficulties in your marital relations by following these tips. If you want to discuss any further issues, you may ask me Direct question.
Wish you a happy and enjoyable marital life.
DR. Nishikant Shrotri